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References

Published online by Cambridge University Press:  05 November 2015

Jan Zaanen
Affiliation:
Universiteit Leiden
Yan Liu
Affiliation:
Universidad Autónoma de Madrid
Ya-Wen Sun
Affiliation:
Universidad Autónoma de Madrid
Koenraad Schalm
Affiliation:
Universiteit Leiden
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References

[1] J. M., Maldacena, “The large N limit of super-conformal field theories and supergravity,Adv. Theor. Math. Phys. 2, 231 (1998) [republished Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:9711200 [hep-th]].Google Scholar
[2] S. S., Gubser, I. R., Klebanov and A. M., Polyakov, “Gauge theory correlators from noncritical string theory,Phys. Lett. B 428, 105 (1998) [arXiv:9802109 [hep-th]].Google Scholar
[3] E., Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:9802150 [hep-th]].Google Scholar
[4] Y., Nakayama, “A lecture note on scale invariance vs conformal invariance” [arXiv:1302.0884 [hep-th]].
[5] J., McGreevy, “Holographic duality with a view toward many-body physics,” Adv.High Energy Phys. 2010, 723105 (2010) [arXiv:0909.0518 [hep-th]].Google Scholar
[6] P., Breitenlohner and D. Z., Freedman, “Positive energy in anti-de Sitter backgrounds and gauged extended supergravity,” Phys. Lett. B 115, 197 (1982).Google Scholar
[7] O., Aharony, S. S., Gubser, J. M., Maldacena, H., Ooguri and Y., Oz, “Large N field theories, string theory and gravity,” Phys. Rep. 323, 183 (2000) [arXiv:9905111 [hep-th]].Google Scholar
[8] J., Erdmenger and H., Osborn, “Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions,” Nucl. Phys. B 483, 431 (1997) [arXiv:9605009 [hep-th]].Google Scholar
[9] M., Ammon and J., Erdmenger, Gauge/Gravity Duality: Foundations and Applications, Cambridge University Press, 2014.
[10] M., Natsuume, “AdS/CFT duality user guide” [arXiv:1409.3575 [hep-th]].
[11] J., Casalderrey-Solana, H., Liu, D., Mateos, K., Rajagopal and U. A., Wiedemann, “Gauge/string duality, hot QCD and heavy ion collisions” [arXiv:1101.0618 [hepth]] (preliminary version of [12]).
[12] J., Casalderrey-Solana, H., Liu, D., Mateos, K., Rajagopal and U. A., Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, Cambridge University Press, 2014.
[13] J. M., Maldacena, “TASI 2003 lectures on AdS/CFT,” in TASI 2003 Proceedings, World Scientific, 2004 [arXiv:0309246 [hep-th]].Google Scholar
[14] G. T., Horowitz and J., Polchinski, “Gauge/gravity duality,” in D., Oriti (ed.), Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter, Cambridge University Press, 2009, pp. 169–186 [arXiv:0602037 [gr-qc]].
[15] J., Polchinski, “Introduction to gauge/gravity duality,” in TASI 2010 Proceedings, World Scientific, 2012 [arXiv:1010.6134 [hep-th]].Google Scholar
[16] J., Maldacena, “The gauge/gravity duality” [arXiv:1106.6073 [hep-th]].
[17] S. A., Hartnoll, “Lectures on holographic methods for condensed matter physics,” Class. Quant. Grav. 26, 224002 (2009) [arXiv:0903.3246 [hep-th]].Google Scholar
[18] C. P., Herzog, “Lectures on holographic superfluidity and superconductivity,” J. Phys. A 42, 343001 (2009) [arXiv:0904.1975 [hep-th]].Google Scholar
[19] G. T., Horowitz, Introduction to Holographic Superconductors, Springer, p. 313 (2011) [arXiv:1002.1722 [hep-th]].
[20] S. A., Hartnoll, “Horizons, holography and condensed matter,” in Black Holes in Higher Dimensions, Cambridge University Press, 2011 [arXiv:1106.4324 [hep-th]].
[21] S., Sachdev, “What can gauge–gravity duality teach us about condensed matter physics?Ann. Rev. Condensed Matter Phys. 3, 9 (2012) [arXiv:1108.1197 [cond-mat.str-el]].Google Scholar
[22] N., Iqbal, H., Liu and M., Mezei, “Lectures on holographic non-Fermi liquids and quantum phase transitions,” in TASI 2010 Proceedings, World Scientific, 2012 [arXiv:1110.3814 [hep-th]].Google Scholar
[23] P. M., Chesler and L. G., Yaffe, “Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes,” JHEP 1407, 086 (2014) [arXiv:1309.1439 [hep-th]].Google Scholar
[24] C. P., Herzog, P., Kovtun, S., Sachdev and D. T., Son, “Quantum critical transport, duality, and M-theory,” Phys. Rev. D 75, 085020 (2007) [arXiv:0701036 [hep-th]].Google Scholar
[25] S., Sachdev, Quantum Phase Transitions, 2nd edn, Cambridge University Press, 2011.
[26] I., Herbut, A Modern Approach to Critical Phenomena, Cambridge University Press, 2007.
[27] M., Endres, T., Fukuhara, D., Pekker, M., Cheneau, P., Schauss, C., Gross, E., Demler, S., Kuhr and I., Bloch, “The ‘Higgs’ amplitude mode at the two-dimensional superfluid–Mott insulator transition,” Nature 487, 454 (2012) [arXiv:1204.5183 [cond-mat.quant-gas]].Google Scholar
[28] I. F., Herbut, V., Juričić and O., Vafek, “Relativistic Mott criticality in graphene,” Phys. Rev. B 80, 075432 (2009) [arXiv:0904.1019 [cond-mat.str-el]].Google Scholar
[29] P. H., Ginsparg, “Applied conformal field theory” [ar Xiv:9108028 [hep-th]].
[30] P. Di, Francesco, P., Mathieu and D., Senechal, Conformal Field Theory, Springer, 1997.
[31] M. R., Gaberdiel, “An Introduction to conformal field theory,” Rep. Prog. Phys. 63, 607 (2000) [arXiv:9910156 [hep-th]].Google Scholar
[32] A. B., Zamolodchikov, “‘Irreversibility’ of the flux of the renormalization group in a 2-D field theory,” JETP Lett. 43, 730 (1986).Google Scholar
[33] D. L., Jafferis, I. R., Klebanov, S. S., Pufu and B. R., Safdi, “Towards the Ftheorem: N = 2 field theories on the three-sphere,” JHEP 1106, 102 (2011) [arXiv:1103.1181 [hep-th]].Google Scholar
[34] Z., Komargodski and A., Schwimmer, “On renormalization group flows in four dimensions,” JHEP 1112, 099 (2011) [arXiv:1107.3987 [hep-th]].Google Scholar
[35] H., Elvang, D. Z., Freedman, L.-Y., Hung, M., Kiermaier, R. C., Myers and S., Theisen, “On renormalization group flows and the a-theorem in 6d,” JHEP 1210, 011 (2012) [arXiv:1205.3994 [hep-th]].Google Scholar
[36] A. J., Beekman, D., Sadri and J., Zaanen, “Condensing Nielsen–Olesen strings and the vortex–boson duality in 3+1 and higher dimensions,” New J. Phys. 13, 033004 (2011) [arXiv:1006.2267 [cond-mat.str-el]].Google Scholar
[37] A. J., Beekman and J., Zaanen, “Electrodynamics of Abrikosov vortices: the field theoretical formulation,” Frontiers Phys. 6, 357 (2011) [arXiv:1106.3946 [condmat. supr-con]].Google Scholar
[38] M., Edalati, R. G., Leigh and P. W., Phillips, “Dynamically generated Mott gap from holography,” Phys. Rev. Lett. 106, 091602 (2011) [arXiv:1010.3238 [hep-th]].Google Scholar
[39] S., Chakravarty, B. I., Halperin and D. R., Nelson, “Two-dimensional quantum Heisenberg antiferromagnet at low temperatures,” Phys. Rev. B 39, 2344 (1989).Google Scholar
[40] E., Fradkin, Field Theories of Condensed Matter Physics, Cambridge University Press, 2013.
[41] T., Senthil, A., Vishwanat, L., Balents, S., Sachdev and M. P. A., Fisher, “Deconfined quantum critical points,” Science 303, 1490 (2004) [arXiv:cond-mat/0311326 [cond-mat.str-el]].Google Scholar
[42] L., Zhu, M., Garst, A., Rosch and Q., Si, “Universally diverging Gruneisen parameter and the magnetocaloric effect close to quantum critical points,” Phys. Rev. Lett. 91, 066404 (2003) [arXiv:0212335 [cond-mat.str-el]].Google Scholar
[43] J., Zaanen and B., Hosseinkhani, “Thermodynamics and quantum criticality in cuprate superconductors,” Phys. Rev. B 70, 060509 (2004) [arXiv:0403345 [condmat.supr-con]].Google Scholar
[44] R., Küchler, N., Oeschler, P., Gegenwart, T., Cichorek, K., Neumaier, O., Tegus, C., Geibel, J. A., Mydosh, F., Steglich, L., Zhu and Q., Si, “Divergence of the Gruneisen ratio at quantum critical points in heavy fermion metals,” Phys. Rev. Lett. 91, 066405 (2003).Google Scholar
[45] J., Zaanen, “Superconductivity: why the temperature is high,” Nature 430, 512 (2004).Google Scholar
[46] G., Policastro, D. T., Son and A. O., Starinets, “The shear viscosity of strongly coupled N = 4 supersymmetric Yang–Mills plasma,” Phys. Rev. Lett. 87, 081601 (2001) [arXiv:0104066 [hep.th]].Google Scholar
[47] M. A., Nielsen and I. L., Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.
[48] X. G., Wen, Quantum Field Theory ofMany Body Systems: From the Origin of Sound to an Origin of Light and Electrons, Oxford University Press, 2004.
[49] T., Chakraborty and P., Pietiläinen, The Fractional Quantum Hall Effect: Properties of an Incompressible Quantum Fluid, Springer, 2012.
[50] J., Nissinen and C. A., Lütken, “The quantum Hall curve,” [arXiv:1207.4693 [condmat.str-el]].
[51] A., Achucarro and P., Townsend, “A Chern–Simons action for three-dimensional anti-de Sitter supergravity theories,” Phys. Lett. B 180, 89 (1986).Google Scholar
[52] E., Witten, “(2 + 1)-Dimensional gravity as an exactly soluble system,” Nucl. Phys. B 311, 46 (1988).Google Scholar
[53] J. de, Boer and J. I., Jottar, “Entanglement entropy and higher spin holography in AdS3,” JHEP 1404, 089 (2014) [arXiv:1306.4347 [hep-th]].Google Scholar
[54] B. de, Wit and H., Nicolai, “N = 8 supergravity,” Nucl. Phys. B 208, 323 (1982).Google Scholar
[55] M., Ammon, A., Castro and N., Iqbal, “Wilson lines and entanglement entropy in higher spin gravity,” JHEP 1310, 110 (2013) [arXiv:1306.4338 [hep-th]].Google Scholar
[56] C., Nayak, S. H., Simon, A., Stern, M., Freedman and S., Das Sarma, “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083 (2008) [arXiv:0707.1889 [cond-mat.str-el]].Google Scholar
[57] M. Z., Hasan and C. L., Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82, 3045 (2010).Google Scholar
[58] X.-L., Qi and S. C., Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1057 (2011) [arXiv:1008.2026 [cond-mat.mes-hall]].Google Scholar
[59] R. J., Slager, A., Mesaros, V., Juričić and J., Zaanen, “The space group classification of topological band insulators,” Nature Physics 9, 98 (2013) [arXiv:1209.2610 [condmat. mes-hall]].Google Scholar
[60] X. L., Qi, T. L., Hughes and S. C., Zhang, “Topological field theory of timereversal invariant insulators,” Phys. Rev. B 78, 195424 (2008) [arXiv:0802.3537 [cond-mat.mes-hall]].Google Scholar
[61] C. W. J., Beenakker, “Search for Majorana fermions in superconductors,” Ann. Rev. Condensed. Matter Phys. 4, 113 (2013) [arXiv:1112.1950 [cond-mat.mes-hall]].Google Scholar
[62] C., Wang, A. C., Potter and T., Senthil, “Classification of interacting electronic topological insulators in three dimensions,” Science 343, 6171 (2014) [arXiv:1306.3238 [cond-mat.str-el]].Google Scholar
[63] H., Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets, World Scientific, 2009.
[64] J., Zaanen, F., Kruger, J.-H., She, D., Sadri and S. I., Mukhin, “Pacifying the Fermi-liquid: battling the devious fermion signs,” Iranian J. Phys. 8, 39 (2008) [arXiv:0802.2455 [cond-mat.other]].Google Scholar
[65] M., Troyer and U.-J., Wiese, “Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations,” Phys. Rev. Lett. 94, 170201 (2005) [arXiv:0408370 [cond-mat]].Google Scholar
[66] R., Shankar, “Renormalization group approach to interacting fermions,” Rev. Mod. Phys. 66, 129 (1994).Google Scholar
[67] J., Polchinski, “Effective field theory and the Fermi surface,” in TASI 1992 Proceedings, [arXiv:9210046 [hep-th]].
[68] G., Baym and C., Pethik, Landau Fermi Liquid Theory, Concepts and Applications, Wiley, 2004.
[69] W. R., Abel, A. C., Anderson and J. C., Wheatley, “Propagation of zero sound in liquid He3 at low temperatures,” Phys. Rev. Lett. 17, 74 (1966).Google Scholar
[70] P. R., Roach and J. B., Ketterson, “Observation of transverse zero sound in normal 3He,” Phys. Rev. Lett. 36, 736 (1976).Google Scholar
[71] J.-H., She and J., Zaanen, “BCS superconductivity in quantum critical metals,” Phys. Rev. B 80, 184518 (2009).Google Scholar
[72] J.-H., She, B. J., Overbosch, Y.-W., Sun, Y., Liu, K., Schalm, J. A., Mydosh and J., Zaanen, “Observing the origin of superconductivity in quantum critical metals,” Phys. Rev. B 84, 144527 (2011) [arXiv:1105.5377 [cond-mat.str-el]].Google Scholar
[73] A. A., Abrikosov, L. P., Gor'kov, and I. Ye., Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics, 2nd edn, Pergamon Press, 1965.
[74] J. A., Hertz, “Quantum critical phenomena,” Phys. Rev. B 14, 1165 (1976).Google Scholar
[75] T., Moriya and A., Kawabate, “Effect of spin fluctuations on itinerant electron ferromagnetism,” J. Phys. Soc. Japan 34, 639 (1973).Google Scholar
[76] A. J., Millis, “Effect of a nonzero temperature on quantum critical points in itinerant fermion systems,” Phys. Rev. B 48, 7183 (1993).Google Scholar
[77] H. von, Löhneisen, A., Rosch, M., Vojta and P., Wölfle, “Fermi-liquid instabilities at magnetic quantum phase transitions,” Rev. Mod. Phys. 79, 1015 (2007).Google Scholar
[78] E.-G., Moon and A. V., Chubukov, “Quantum-critical pairing with varying exponents,” J. Low Temp. Phys. 161, 263 (2010) [arXiv:1005.0356 [cond-mat.suprcon]].Google Scholar
[79] S. A., Hartnoll, D. M., Hofman, M. A., Metlitski and S., Sachdev, “Quantum critical response at the onset of spin density wave order in two-dimensional metals,” Phys. Rev. B 84, 125115 (2011) [arXiv:1106.0001 [cond-mat.str-el]].Google Scholar
[80] S.-S., Lee, “Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions,” Phys. Rev. B 80, 165102 (2009) [arXiv:0905.4532 [condmat.str-el]].Google Scholar
[81] M. A., Metlitski and S. Sachdev, “Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order,” Phys. Rev. B 82, 075128 (2010) [arXiv:1005.1288 [cond-mat.str-el]].Google Scholar
[82] D., Dalidovich and S.-S., Lee, “Perturbati-ve non-Fermi liquids from dimensional regularization,” Phys. Rev. B 88, 245106 (2013) [arXiv:1307.3170 [cond-mat.strel]].Google Scholar
[83] A. L., Fitzpatrick, S., Kachru, J., Kaplan and S., Raghu, “Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals,” Phys. Rev. B 88, 125116 (2013) [arXiv:1307.0004 [cond-mat.str-el]].Google Scholar
[84] T., Senthil and M. P. A., Fisher, “Z2 gauge theory of electron fractionalization in strongly correlated systems,” Phys. Rev. B 62, 7850 (2000) [arXiv:9910224 [condmat.str-el]].Google Scholar
[85] E., Berg, M. A., Metlitski and S., Sachdev, “Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals,” Science 338, 1606 (2012) [arXiv:1206.0742 [cond-mat.str-el]].
[86] P. W., Anderson, The Theory of High-Tc Superconductivity, Princeton University Press, 1997.
[87] J., Zaanen, “A modern, but way too short history of the theory of superconductivity at a high temperature,” in H., Rogalla and P. H., Kes (eds), 100 Years of Superconductivity, CRC Press, 2012, pp. 92–114 [arXiv:1012.5461 [cond-mat.supr-con]].
[88] H., Liu, “From black holes to strange metals,” Physics Today 65, 68 (2012).Google Scholar
[89] S. V., Kravchenko and M. P., Sarachik, “Metal–insulator transition in twodimensional electron systems,” Rep. Prog. Phys. 67, 1 (2004).Google Scholar
[90] O., Gunnarsson and K., Schönhammer, “Electron spectroscopies for Ce compounds in the impurity model,” Phys. Rev. B 28, 4315 (1983).Google Scholar
[91] J. W., Allen, S. J., Oh, O., Gunnarsson, K., Schönhammer, M. B., Maple, M. S., Torikachvili and I., Lindau, “Electronic structure of cerium and light rare-earth intermetallics,” Adv. Phys. 35, 275 (1986).Google Scholar
[92] J., Zaanen, G. A., Sawatzky and J. W., Allen, “Band gaps and electronic structure of transition-metal compounds,” Phys. Rev. Lett. 55, 418 (1985).Google Scholar
[93] V. I., Anisimov, J., Zaanen and O. K., Andersen, “Band theory and Mott insulators: Hubbard U instead of Stoner I,” Phys. Rev. B 44, 943 (1991).Google Scholar
[94] J., Zaanen and A. M., Oles, “Canonical perturbation theory and the two band model for high-Tc superconductors,” Phys. Rev. B 37, 9423 (1988).Google Scholar
[95] A. C., Hewson, The Kondo Problem to Heavy Fermions, Cambridge University Press, 1993.
[96] P., Phillips, “Mottness: identifying the propagating charge modes in doped Mott insulators,” Rev. Mod. Phys. 82, 1719 (2010) [arXiv:1001.5270 [cond-mat.str-el]].Google Scholar
[97] Z.-Y., Weng, “Mott physics, sign structure, ground state wavefunction, and high-Tc superconductivity,” Frontiers Phys. 6, 370 (2011) [arXiv:1110.0546 [cond-mat.supr-con]].Google Scholar
[98] J., Zaanen and B. J., Overbosch, “Mottness collapse and statistical quantum criticalityPhil. Trans. R. Soc. A 369, 1599 (2011) [arXiv:0911.4070[cond-mat.str-el]].Google Scholar
[99] Z., Zhu, H.-C., Jiang, Y., Qi, C.-S., Tian and Z.-Y., Weng, “Strong correlation induced charge localization in antiferromagnets,” Sci. Rep. 3, 2586 (2013) [arXiv:1212.6634[cond-mat.str-el]].Google Scholar
[100] Z., Zhu, H.-C., Jiang, D.-N., Sheng and Z.-Y., Weng, “Hole binding in Mott antiferromagnets: a DMRG study” [arXiv:1312.6893 [cond-mat.str-el]].
[101] P. W., Anderson, “The resonating valence bond state in La2CuO4 and superconductivity,” Science 235, 1196 (1987).Google Scholar
[102] T. H., Hansson, V., Oganesyan and S. L., Sondhi, “Superconductors are topologically ordered,” Annals of Physics 313, 497 (2004) [arXiv:cond-mat/0404327 [cond-mat.supr-con]].Google Scholar
[103] J. B., Kogut, “An introduction to lattice gauge theory and spin systems,” Rev. Mod. Phys. 51, 659 (1979).Google Scholar
[104] M., Levin and X.-G., Wen, “String-net condensation: a physical mechanism for topological phases,” Phys. Rev. B 71, 045110 (2005) [arXiv:0404617 [cond-mat.str-el]].Google Scholar
[105] S., Sachdev, “The quantum phases of matter” [arXiv:1203.4565 [hep-th]].
[106] S. A., Kivelson, D. S., Rohksar and J. P., Sethna, “Topology of the resonating valencebond state: solitons and high-Tc superconductivity,” Phys. Rev. B 35, 8865 (1987).Google Scholar
[107] R., Moessner and S. L., Sondhi, “Resonating valence bond phase in the triangular lattice quantum dimer model,” Phys. Rev. Lett. 86, 1881 (2001).Google Scholar
[108] X. G., Wen, “Mean-field theory of spin-liquid states with finite energy gap and topological orders,” Phys. Rev. B 44, 2664 (1991).Google Scholar
[109] N., Read and S., Sachdev, “Large-N expansion for frustrated quantum antiferromagnets,” Phys. Rev. Lett. 66, 1773 (1991).Google Scholar
[110] A., Kitaev, “Anyons in an exactly solved model and beyond,” Annals of Physics, 321, 2 (2006) [arXiv:0506438 [cond-mat.mes-hall]].Google Scholar
[111] L., Balents, “Spin liquids in frustrated magnets,” Nature 464, 199 (2010).Google Scholar
[112] P. A., Lee, N., Nagoasa and X.-G., Wen, “Doping a Mott insulator: physics of high temperature superconductivity,” Rev. Mod. Phys. 78, 17 (2006) [arXiv:condmat/0410445 [cond-mat.str-el]].Google Scholar
[113] X.-G., Wen, “Quantum orders and symmetric spin liquids,” Phys. Rev. B 65, 165113 (2002) [arXiv:0107071 [cond-mat.str-el]].Google Scholar
[114] P., Coleman, “Heavy fermions: electrons at the edge of magnetism,” in H., Kronmuller and S., Parkin (eds.), Handbook of Magnetism and Advanced Magnetic Materials. Volume 1: Fundamentals and Theory, John Wiley and Sons, 2007, pp. 95–148 [arXiv:0612006 [cond-mat.str-el]].
[115] B., Keimer, S. A., Kivelson, M. R., Norman, S., Uchida and J., Zaanen, “From quantum matter to high temperature superconductivity in copper oxides,” Nature 518, 179 (2015).Google Scholar
[116] S., Raghu, S. A., Kivelson and D. J., Scalapino, “Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution,” Phys. Rev. B 81, 224505 (2010).Google Scholar
[117] D. J., Scalapino, “A common thread: the pairing interaction for the unconventional superconductors,” Rev. Mod. Phys. 84, 1383 (2012) [arXiv:1207.4093 [cond-mat.supr-con]].Google Scholar
[118] C. M., Varma, “Considerations on the mechanisms and transition temperatures of superconductors,” Rep. Prog. Phys. 75, 052501 (2012) [arXiv:1001.3618 [condmat.supr-con]].Google Scholar
[119] M. R., Norman, “The challenge of unconventional superconductivity,” Science 332, 196 (2011).Google Scholar
[120] N. F., Berk and J. R., Schrieffer, “Effect of ferromagnetic spin correlations on superconductivity,” Phys. Rev. Lett. 17, 433 (1966).Google Scholar
[121] C. N. A., van Duin and J., Zaanen, “Interplay of superconductivity and magnetism in strong coupling,” Phys. Rev. B 61, 3676 (2000).Google Scholar
[122] S. R., White, “Density matrix formulation for quantum renormalization groups,” Phys. Rev. Lett. 69, 2863 (1992).Google Scholar
[123] U., Schollwoeck, “The density-matrix renormalization group,” Rev. Mod. Phys. 77, 259 (2005) [arXiv:0409292 [cond-mat.str-el]].Google Scholar
[124] F., Verstraete, J. I., Cirac and V., Murg, “Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems,” Adv. Phys. 57, 143 (2008).Google Scholar
[125] P., Corboz, R., Orus, B., Bauer and G., Vidal, “Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states,” Phys. Rev. B 81, 165104 (2010) [arXiv:0912.0646 [cond-mat.str-el]].Google Scholar
[126] P., Corboz, T. M., Rice and M., Troyer, “Competing states in the t–J model: uniform d-wave state versus stripe state” [arXiv:1402.2859 [cond-mat.str-el]].
[127] S. R., White and D. J., Scalapino, “Density matrix renormalization group study of the striped phase in the 2D t–J Model,” Phys. Rev. Lett. 80, 1272 (1998).Google Scholar
[128] J., Zaanen and O., Gunnarsson, “Charged magnetic domain lines and the magnetism of the High-Tc superconducting oxides,” Phys. Rev. B 40, 7391 (1989).Google Scholar
[129] K., Machida, “Magnetism in La2CuO4 based compounds,” PhysicaC 158, 192 (1989).Google Scholar
[130] A. J., Heeger, S. A., Kivelson, J. R., Schrieffer and W.-P., Su, “Solitons in conducting polymers,” Rev. Mod. Phys. 60, 781 (1988).Google Scholar
[131] J. M., Tranquada, B. J., Sternlieb, J. D., Axe, Y., Nakamura and S., Uchida, “Evidence for stripe correlations of spins and holes in copper oxide superconductors,” Nature 375, 561 (1995).Google Scholar
[132] M., Vojta, “Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity,” Adv. Phys. 58, 699 (2009) [arXiv:0901.3145 [condmat. supr-con]].Google Scholar
[133] W., Metzner and D., Vollhardt, “Correlated lattice fermions in d = ∞dimensions,” Phys. Rev. Lett. 62, 324 (1989).Google Scholar
[134] A., Georges and G., Kotliar, “Hubbard model in infinite dimensions,” Phys. Rev. B 45, 6479 (1992).Google Scholar
[135] G., Kotliar and D., Vollhardt, “Strongly correlated materials: insights from dynamical mean-field theory,” Physics Today 57, 53 (2004).Google Scholar
[136] A., Georges, G., Kotliar, W., Krauth and M. J., Rozenberg, “Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions,” Rev. Mod. Phys. 68, 13 (1996).Google Scholar
[137] G., Kotliar, S., Savrasov, K., Haule, V., Oudovenko, O., Parcollet and C., Matianetti, “Electronic structure calculations with dynamical mean-field theory,” Rev. Mod. Phys. 78, 865 (2006).Google Scholar
[138] T., Maier, M., Jarrell, T., Pruschke and M. H., Hettler, “Quantum cluster theories,” Rev. Mod. Phys. 77, 1027 (2005).Google Scholar
[139] S.-X., Yang, H., Fotso, S.-Q., Su, D., Galanakis, E., Khatami, J.-H., She, J., Moreno, J., Zaanen and M., Jarrell, “Proximity of the superconducting dome and the quantum critical point in the two-dimensional Hubbard model,” Phys. Rev. Lett. 106, 047004 (2011).Google Scholar
[140] C., Pfleiderer, “Superconducting phases of f-electron compounds,” Rev. Mod. Phys. 81, 1551 (2009) [arXiv:0905.2625 [cond-mat.supr-con]].Google Scholar
[141] P., Gegenwart, Q., Si and F., Steglich, “Quantum criticality in heavy-fermion metals,” Nature Physics 4, 186 (2008).Google Scholar
[142] J., Zaanen, “Quantum critical electron systems: The uncharted sign worlds,” Science 319, 1205 (2008).Google Scholar
[143] A. R., Schmidt, M. H., Hamidian, P., Wahl, F., Meier, A. V., Balatsky, J. D., Garrett, T. J., Williams, G. M., Luke and J. C., Davis, “Imaging the Fano lattice to ‘hidden order’ transition in URu2Si2,” Nature 465, 570 (2010).Google Scholar
[144] P., Aynajian, E. H. da Silva, Neto, A., Gyenis, R. E., Baumbach, J. D., Thompson, Z., Fisk, E. D., Bauer and A., Yazdani, “Visualizing heavy fermions emerging in a quantum critical Kondo lattice,” Nature 486, 201 (2012).Google Scholar
[145] A., Schröder, G., Aeppli, E., Bucher, R., Ramazashvili and P., Coleman, “Scaling of magnetic fluctuations near a quantum phase transition,” Phys. Rev. Lett. 80, 5623 (1998).Google Scholar
[146] A., Schröder, G., Aeppli, R., Coldea, M., Adams, O., Stockert, H. von, Löhneysen, E., Bucher, R., Ramazashvili and P., Coleman, “Onset of antiferromagnetism in heavyfermion metals,” Nature 407, 351 (2000).Google Scholar
[147] P., Coleman, A. J., Schofield and A. M., Tsvelik, “How should we interpret the two transport relaxation times in the cuprates?J. Phys.: Condensed Matter 8, 9985 (1996) [arXiv:9609009 [cond-mat]].
[148] J., Zaanen, “Holographic duality: stealing dimensions from metals,” Nature Physics 9, 609 (2013).Google Scholar
[149] D. van der, Marel, H. J. A., Molegraaf, J., Zaanen, Z., Nussinov, F., Carbone, A., Damascelli, H., Eisaki, M., Greven, P. H., Kes and M., Li, “Power-law optical conductivity with a constant phase angle in high Tc superconductors,” Nature 425, 271 (2003) [arXiv:0309172 [cond-mat.mes-hall]].Google Scholar
[150] K., Fujita, C. K., Kim, I., Lee, J., Lee, M. H., Hamidian, I. A., Firmo, S., Mukhopadhyay, H., Eisaki, S., Uchida, M. J., Lawler, E.-A., Kim and J. C., Davis, “Simultaneous transition in cuprate momentum-space topology and electronic symmetry breaking,” Science 344, 613 (2014) [arXiv:1403.7788 [cond-mat.supr-con]].Google Scholar
[151] U., Chatterjee, D., Ai, J., Zhao, S., Rosenkranz, A., Kaminski, H., Raffy, Z., Li, K., Kadowaki, M., Randeria, M. R., Norman and J. C., Campuzano, “Electronic phase diagram of high-temperature copper oxide superconductors,” PNAS 108, 9346 (2011).Google Scholar
[152] C. M., Varma, P. B., Littlewood, S., Schmitt-Rink, E., Abrahams and A. E., Ruckenstein, “Phenomenology of the normal state of Cu–O high-temperature superconductors,” Phys. Rev. Lett. 63, 1996 (1989).Google Scholar
[153] R. A., Cooper, Y., Wang, B., Vignolle, O. J., Lipscombe, S. M., Hayden, Y., Tanabe, T., Adachi, Y., Koike, M., Nohara, H., Takagi, C., Proust and N. E., Hussey, “Anomalous criticality in the electrical resistivity of La2−x SrxCuO4,” Science 323, 603 (2009).Google Scholar
[154] K., Fujita, M. H., Hamidian, S. D., Edkins, C. K., Kim, Y., Kohsaka, M., Azuma, M., Takano, H., Takagi, H., Eisaki, S., Uchida, A., Allais, M. J., Lawler, E.-A., Kim, S., Sachdev and J. C. Seamus, Davis, “Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates,” PNAS 111, E3026 (2014) [arXiv:1404.0362 [cond-mat.supr-con]].Google Scholar
[155] J., Zaanen, “High temperature superconductivity: the sound of the hidden order,” Nature 498, 41 (2013).Google Scholar
[156] I. M., Vishik, E. A., Nowadnick, W. S., Lee, Z. X., Shen, B., Moritz, T. P., Devereaux, K., Tanaka, T., Sasagawaand T., Fujii, “A momentum-dependent perspective on quasiparticle interference in Bi2Sr2CaCu2O8+δ,” Nature Physics 5, 718 (2009) [arXiv:0909.0762 [cond-mat.supr-con]].Google Scholar
[157] Y., He, Y., Yin,M., Zech, A., Soumyanarayanan, M. M., Yee, T., Williams,M. C., Boyer, K., Chatterjee,W. D., Wise, I., Zeljkovic, T., Kondo, T., Takeuchi, H., Ikuta, P., Mistark, R. S., Markiewicz, A., Bansil, S., Sachdev, E. W., Hudson and J. E., Hoffman, “Fermi surface and pseudogap evolution in a cuprate superconductor,” Science 344, 608 (2014).Google Scholar
[158] R., Comin, A., Frano, M. M., Yee, Y., Yoshida, H., Eisaki, E., Schierle, E., Weschke, R., Sutarto, F., He, A., Soumyanarayanan, Yang, He, M. Le, Tacon, I. S., Elfimov, J. E., Hoffman, G. A., Sawatzky, B., Keimerand A., Damascelli, “Charge order driven by Fermi-arc instability in Bi2Sr2xLaxCuO6+δ,Science 343, 390 (2014).Google Scholar
[159] N., Iqbal, H., Liu and M., Mezei, “Semi-local quantum liquids,” JHEP 1204, 086 (2012) [arXiv:1105.4621 [hep-th]].Google Scholar
[160] N., Iqbal, H., Liu and M., Mezei, “Quantum phase transitions in semi-local quantum liquids” [arXiv:1108.0425 [hep-th]]
[161] S. W., Hawking and G. F. R., Ellis, The Large Scale Structure of Space-time, Cambridge University Press, 1973.
[162] S., Hawking and R., Penrose, The Nature of Space and Time, Princeton University Press, 1996.
[163] C. W., Misner, K. S., Thorne and J. A., Wheeler, Gravitation, W. H. Freeman and Company, 1973.
[164] J. D., Bekenstein, “Black hole hair: 25 years after,” in Second International A. D. Sakharov Conference on Physics, 1996, pp. 216–219 [arXiv:9605059 [gr-qc]].Google Scholar
[165] J. M., Bardeen, B., Carter and S. W., Hawking, “The four laws of black hole mechanics,” Commun. Math. Phys. 31, 161 (1973).Google Scholar
[166] J. D., Bekenstein, “Black holes and entropy,” Phys. Rev. D 7, 2333 (1973).Google Scholar
[167] G. 't, Hooft, “Dimensional reduction in quantum gravity” [arXiv:9310026 [gr-qc]].
[168] L., Susskind, “The world as a hologram,” J. Math. Phys. 36, 6377 (1995)[arXiv:9409089 [hep-th]].Google Scholar
[169] A., Strominger and C., Vafa, “Microscopic origin of the Bekenstein–Hawking entropy,” Phys. Lett. B 379, 99 (1996) [arXiv:9601029 [hep-th]].Google Scholar
[170] M. B., Green, J. H., Schwarz and E., Witten, Superstring Theory. Volume 1: Introduction and Superstring Theory. Volume 2: Loop Amplitudes, Anomalies and Phenomenology, Cambridge University Press, 1987.
[171] J., Polchinski, String Theory. Volume 1: An Introduction to the Bosonic String, Cambridge University Press, 1998.
[172] J., Polchinski, String Theory. Volume 2: Superstring Theory and Beyond, Cambridge University Press, 1998.
[173] A. N., Schellekens, “Life at the interface of particle physics and string theory,” Rev. Mod. Phys. 85, 1491 (2013) [arXiv:1306.5083 [hep-ph]].Google Scholar
[174] N., Seiberg, “Emergent spacetime” [arXiv:0601234 [hep-th]].
[175] J., Polchinski, “Dirichlet branes and Ramond–Ramond charges,” Phys. Rev. Lett. 75, 4724 (1995) [arXiv:9510017 [hep-th]].Google Scholar
[176] N., Arkani-Hamed, S., Dimopoulos and G. R., Dvali, “The hierarchy problem and new dimensions at a millimeter,” Phys. Lett. B 429, 263 (1998) [arXiv:9803315 [hep-th]].Google Scholar
[177] G., Shiu and S. H. H., Tye, “TeV scale superstring and extra dimensions,” Phys. Rev. D 58, 106007 (1998) [arXiv:9805157 [hep-th]].Google Scholar
[178] R., Maartens and K., Koyama, “Brane-world gravity,” Living Rev. Rel. 13, 5 (2010) [arXiv:1004.3962 [hep-th]].Google Scholar
[179] N., Beisert and M., Staudacher, “The N=4 SYM integrable super spin chain,” Nucl. Phys. B 670, 439 (2003) [arXiv:0307042 [hep-th]].Google Scholar
[180] A., Cappelli and I. D., Rodriguez, “Matrix effective theories of the fractional quantum Hall effect,” J. Phys. A 42, 304006 (2009) [arXiv:0902.0765 [hep-th]].Google Scholar
[181] S.-S., Lee, “Low-energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions,” Phys. Rev. B 80, 165102 (2009) [arXiv:0905.4532 [condmat. str-el]].Google Scholar
[182] A. Liam, Fitzpatrick, S., Kachru, J., Kaplan and S., Raghu, “Non-Fermi liquid behavior of large NB quantum critical metals,” Phys. Rev. B 89, 165114 (2014) [arXiv:1312.3321 [cond-mat.str-el]].Google Scholar
[183] S., Coleman, Aspects of Symmetry, Cambridge University Press, 1985.
[184] J., Zinn-Justin, Quantum Field Theory and Critical Phenomena, 4th edn, Clarendon Press, 2002.
[185] M., Moshe and J., Zinn-Justin, “Quantum field theory in the large-N limit: a review,” Phys. Rep. 385, 69 (2003) [arXiv:0306133 [hep-th]].Google Scholar
[186] G. 't, Hooft, “A planar diagram theory for strong interactions,” Nucl. Phys. B 72, 461 (1974).Google Scholar
[187] A. V., Manohar, “Large N QCD” [arXiv:9802419 [hep-ph]].
[188] A. V., Ramallo, “Introduction to the AdS/CFT correspondence,” in C. Merino (ed.), Lectures on Particle Physics, Astrophysics and Cosmology, Proceedings of the Third IDPASC School, Santiago de Compostela, Springer, 2015, 411 [arXiv:1310.4319 [hep-th]].
[189] E., Witten, “The 1/N expansion in atomic and particle physics,” in G. 't Hooft (ed.), Recent Developments in Gauge Theories, Cargèse Lectures, Plenum, 1980, HUTP-79/A078.
[190] E., Brezin and S. R., Wadia, The Large N Expansion in Quantum Field Theory and Statistical Physics: From Spin Systems to Two-Dimensional Gravity, World Scientific, 1993.Google Scholar
[191] D. J., Gross and W., Taylor, “Two-dimensional QCD is a string theory,” Nucl. Phys. B 400, 181 (1993) [arXiv:9301068 [hep-th]].Google Scholar
[192] J., Polchinski, “Scale and conformal invariance in quantum field theory,” Nucl. Phys. B 303, 226 (1988).Google Scholar
[193] D., Dorigoni and V. S., Rychkov, “Scale invariance + unitarity => conformal invariance?” [arXiv:0910.1087 [hep-th]].
[194] M. A., Luty, J., Polchinski and R., Rattazzi, “The a-theorem and the asymptotics of 4D quantum field theory,” JHEP 1301, 152 (2013) [arXiv:1204.5221 [hep-th]].Google Scholar
[195] S., Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons, 1972.
[196] R. M., Wald, General Relativity, Chicago University Press, 1984.
[197] S. M., Carroll, Spacetime and geometry: An Introduction to General Relativity, Addison-Wesley, 2004.
[198] V., Balasubramanian, P., Kraus and A. E., Lawrence, “Bulk versus boundary dynamics in anti-de Sitter space-time,” Phys. Rev. D 59, 046003 (1999) [arXiv:9805171 [hep-th]].Google Scholar
[199] J. L., Petersen, “Introduction to the Maldacena conjecture on AdS/CFT,” Int. J. Mod. Phys. A 14, 3597 (1999) [arXiv:9902131 [hep-th]].Google Scholar
[200] S. de, Haro, S. N., Solodukhin and K., Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence,” Commun. Math. Phys. 217, 595 (2001) [arXiv:0002230 [hep-th]].Google Scholar
[201] D. T., Son and A. O., Starinets, “Minkowski space correlators in AdS/CFT correspondence: recipe and applications,” JHEP 0209, 042 (2002) [arXiv:0205051 [hep-th]].Google Scholar
[202] C. P., Herzog and D. T., Son, “Schwinger–Keldysh propagators from AdS/CFT correspondence,” JHEP 0303, 046 (2003) [arXiv:0212072 [hep-th]].Google Scholar
[203] D. Z., Freedman, S. D., Mathur, A., Matusis and L., Rastelli, “Correlation functions in the CFT(d)/AdS(d + 1) correspondence,” Nucl. Phys. B 546, 96 (1999) [arXiv:9804058 [hep-th]].Google Scholar
[204] K., Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19, 5849 (2002) [arXiv:0209067 [hep-th]].Google Scholar
[205] E., D'Hoker and D. Z., Freedman, “Supersymmetric gauge theories and the AdS/CFT correspondence,” [arXiv:0201253 [hep-th]].
[206] M. J. G., Veltman, “Unitarity and causality in a renormalizable field theory with unstable particles,” Physica 29, 186 (1963).Google Scholar
[207] S, Minwalla, “Restrictions imposed by super-conformal invariance on quantum field theories,” Adv. Theor. Math. Phys. 2, 781 (1998) [arXiv:9712074 [hep-th]].Google Scholar
[208] J. de, Boer, E. P., Verlinde and H. L., Verlinde, “On the holographic renormalization group,” JHEP 0008, 003 (2000) [arXiv:9912012 [hep-th]].
[209] E., Witten, “Multitrace operators, boundary conditions, and AdS/CFT correspondence” [arXiv:0112258 [hep-th]].
[210] W., Mueck, “An improved correspondence formula for AdS/CFT with multitrace operators,” Phys. Lett. B 531, 301 (2002) [arXiv:0201100 [hep-th]].Google Scholar
[211] E., Witten, “Anti-de Sitter space, thermal phase transition, and confinement in gauge theories,” Adv. Theor. Math. Phys. 2, 505 (1998) [arXiv:9803131 [hep-th]].Google Scholar
[212] G. W., Gibbons and S. W., Hawking (eds), Euclidean Quantum Gravity. World Scientific, 1993.
[213] E., Berti, V., Cardoso and A. O., Starinets, “Quasinormal modes of black holes and black branes,” Class. Quant. Grav. 26, 163001 (2009) [arXiv:0905.2975 [gr-qc]].Google Scholar
[214] D., Birmingham, “Topological black holes in anti-de Sitter space,” Class. Quant. Grav. 16, (1999) [arXiv:9808032 [hep-th]].Google Scholar
[215] S. S., Gubser, I. R., Klebanov and A. A., Tseytlin, “Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang–Mills theory,” Nucl. Phys. B 534, 202 (1998) [arXiv:9805156 [hep-th]].Google Scholar
[216] S. S., Gubser, I. R., Klebanov and A. W., Peet, “Entropy and temperature of black 3-branes,” Phys. Rev. D 54, 3915 (1996) [arXiv:9602135 [hep-th]].Google Scholar
[217] G. W., Gibbons and S. W., Hawking, “Action integrals and partition functions in quantum gravity,” Phys. Rev. D 15, 2752 (1977).Google Scholar
[218] J. W., York, “Role of conformal three-geometry in the dynamics of gravitation,” Phys. Rev. Lett. 28, 1082 (1972).Google Scholar
[219] V., Balasubramanian and P., Kraus, “A stress tensor for anti-de Sitter gravity,” Commun. Math. Phys. 208, 413 (1999) [arXiv:9902121 [hep-th]].Google Scholar
[220] I., Papadimitriou and K., Skenderis, “Thermodynamics of asymptotically locally AdS spacetimes,” JHEP 0508, 004 (2005) [arXiv:0505190 [hep-th]].Google Scholar
[221] S. W., Hawking and D. N., Page, “Thermodynamics of black holes in anti-de Sitter space,” Commun. Math. Phys. 87, 577 (1983).Google Scholar
[222] J. M., Maldacena, “Wilson loops in large-N field theories,” Phys. Rev. Lett. 80, 4859 (1998) [arXiv:9803002 [hep-th]].Google Scholar
[223] S. J., Rey and J. T., Yee, “strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity,” Eur. Phys. J. C 22, 379 (2001) [arXiv:9803001 [hep-th]].Google Scholar
[224] A., Brandhuber, N., Itzhaki, J., Sonnenschein and S., Yankielowicz, “Wilson loops, confinement, and phase transitions in large-N gauge theories from supergravity,” JHEP 9806, 001 (1998) [arXiv:9803263 [hep-th]].Google Scholar
[225] O., Jahn and O., Philipsen, “The Polyakov loop and its relation to static quark potentials and free energies,” Phys. Rev. D 70, 074504 (2004) [arXiv:0407042 [hep-th]].Google Scholar
[226] S.-J., Rey, S., Theisen and J.-T., Yee, “Wilson–Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity,” Nucl. Phys. B 527, 171 (1998) [arXiv:9803135 [hep-th]].Google Scholar
[227] A., Brandhuber, N., Itzhaki, J., Sonnenschein and S., Yankielowicz, “Wilson loops in the large-N limit at finite temperature,” Phys. Lett. B 434, 36 (1998) [arXiv:9803137 [hep-th]].Google Scholar
[228] J., Erlich, “Recent results in AdS/QCD,” PoS Confinement 8, 032 (2008) [arXiv:0812.4976 [hep-th]].Google Scholar
[229] J., Polchinski and M. J., Strassler, “The string dual of a confining four-dimensional gauge theory” [arXiv:0003136 [hep-th]].
[230] I. R., Klebanov and M. J., Strassler, “Supergravity and a confining gauge theory: duality cascades and chi SB resolution of naked singularities,” JHEP 0008, 052 (2000) [arXiv:0007191 [hep-th]].Google Scholar
[231] M., Kruczenski, D., Mateos, R. C., Myers and D. J., Winters, “Towards a holographic dual of large N(c) QCD,” JHEP 0405, 041 (2004) [arXiv:0311270 [hep-th]].Google Scholar
[232] T., Sakai and S., Sugimoto, “Low energy hadron physics in holographic QCD,” Prog. Theor. Phys. 113, 843 (2005) [arXiv:0412141 [hep-th]].Google Scholar
[233] T., Sakai and S., Sugimoto, “More on a holographic dual of QCD,” Prog. Theor. Phys. 114, 1083 (2005) [arXiv:0507073 [hep-th]].Google Scholar
[234] J., Erlich, E., Katz, D. T., Son and M. A., Stephanov, “QCD and a holographic model of hadrons,” Phys. Rev. Lett. 95, 261602 (2005) [arXiv:0501128 [hep-th]].Google Scholar
[235] C. P., Herzog, “A holographic prediction of the deconfinement temperature,” Phys. Rev. Lett. 98, 091601 (2007) [arXiv:0608151 [hep-th]].Google Scholar
[236] L. Da, Rold and A., Pomarol, “Chiral symmetry breaking from five dimensional spaces,” Nucl. Phys. B 721, 79 (2005) [arXiv:0501218 [hep-ph]].Google Scholar
[237] S., Caron-Huot, P., Kovtun, G. D., Moore, A., Starinets and L. G., Yaffe, “Photon and dilepton production in supersymmetric Yang–Mills plasma,” JHEP 0612, 015 (2006) [arXiv:0607237 [hep-th]].Google Scholar
[238] A., Karch, E., Katz, D. T., Son and M. A., Stephanov, “Linear confinement and AdS/QCD,” Phys. Rev. D 74, 015005 (2006) [arXiv:0602229 [hep-th]].Google Scholar
[239] G. T., Horowitz and R. C., Myers, “The AdS/CFT correspondence and a new positive energy conjecture for general relativity,” Phys. Rev. D 59, 026005 (1999) [arXiv:9808079 [hep-th]].Google Scholar
[240] H., Boschi-Filho and N. R. F., Braga, “QCD/string holographic mapping and glueball mass spectrum,” Eur. Phys. J. C 32, 529 (2004) [arXiv:0209080 [hep-th]].Google Scholar
[241] D. K., Hong, T., Inami and H.-U., Yee, “Baryons in AdS/QCD,” Phys. Lett. B 646, 165 (2007) [arXiv:0609270 [hep-th]].Google Scholar
[242] S. S., Gubser, S. S., Pufu and F. D., Rocha, “Bulk viscosity of strongly coupled plasmas with holographic duals,” JHEP 0808, 085 (2008) [arXiv:0806.0407 [hep-th]].Google Scholar
[243] N., Iqbal and H., Liu, “Real-time response in AdS/CFT with application to spinors,” Fortsch. Phys. 57, 367 (2009) [arXiv:0903.2596 [hep-th]].Google Scholar
[244] W., Witczak-Krempa, E., Sorensen and S., Sachdev, “The dynamics of quantum criticality via quantum Monte Carlo and holography,” Nature Physics 10, 361 (2014) [arXiv:1309.2941 [cond-mat.str-el]].Google Scholar
[245] K., Skenderis and B. C. van, Rees, “Real-time gauge/gravity duality: prescription, renormalization and examples,” JHEP 0905, 085 (2009) [arXiv:0812.2909 [hepth]].Google Scholar
[246] G. C., Giecold, “Fermionic Schwinger–Keldysh propagators from AdS/CFT,” JHEP 0910, 057 (2009) [arXiv:0904.4869 [hep-th]].Google Scholar
[247] K., Damle and S., Sachdev, “Non-zero temperature transport near quantum critical points,” Phys. Rev. B 56, 8714 (1997) [arXiv:9705206 [cond-mat.str-el]].Google Scholar
[248] G., Policastro, D. T., Son and A. O., Starinets, “From AdS/CFT correspondence to hydrodynamics,” JHEP 0209, 043 (2002) [arXiv:0205052 [hep-th]].Google Scholar
[249] E., Shuryak, “Why does the quark–gluon plasma at RHIC behave as a nearly ideal fluid?Prog. Part. Nucl. Phys. 53, 273 (2004) [arXiv:0312227 [hep-th]].Google Scholar
[250] D., Teaney, “The effects of viscosity on spectra, elliptic flow, and HBT radii,” Phys. Rev. C 68, 034913 (2003) [arXiv:0301099 [nucl-th]].Google Scholar
[251] E. V., Shuryak, “What RHIC experiments and theory tell us about properties of quark–gluon plasma?,” Nucl. Phys. A 750, 64 (2005) [arXiv:0405066 [hep-th]].Google Scholar
[252] P., Kovtun, D. T., Son and A. O., Starinets, “Viscosity in strongly interacting quantum field theories from black hole physics,” Phys. Rev. Lett. 94, 111601 (2005) [arXiv:0405231 [hep-th]].Google Scholar
[253] S. A., Hartnoll, P. K., Kovtun, M., Muller and S., Sachdev, “Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes,” Phys. Rev. B 76, 144502 (2007) [arXiv:0706.3215 [cond-mat.str-el]].Google Scholar
[254] S., Bhattacharyya, V., Hubeny, S., Minwalla and M., Rangamani, “Nonlinear fluid dynamics from gravity,” JHEP 0802, 045 (2008) [arXiv:0712.2456 [hep-th]].Google Scholar
[255] D., Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, Benjamin, 1975.
[256] L. D., Landau and E. M., Lifshitz, Fluid Mechanics, 2nd edn. Pergamon Press, 1987.
[257] R., Baier, P., Romatschke, D. T., Son, A. O., Starinets and M. A., Stephanov, “Relativistic viscous hydrodynamics, conformal invariance, and holography,” JHEP 0804, 100 (2008) [arXiv:0712.2451 [hep-th]].Google Scholar
[258] L. P, Kadanoff and P. C., Martin, “Hydrodynamic equations and correlation functions,” Annals of Physics 24, 419 (1963).Google Scholar
[259] N., Iqbal and H., Liu, “Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm,” Phys. Rev. D 79, 025023 (2009) [arXiv:0809.3808 [hep-th]].Google Scholar
[260] P., Kovtun, D. T., Son and A. O., Starinets, “Holography and hydrodynamics: diffusion on stretched horizons,” JHEP 0310, 064 (2003) [arXiv:0309213 [hep-th]].Google Scholar
[261] A., Buchel and J. T., Liu, “Universality of the shear viscosity in supergravity,” Phys. Rev. Lett. 93, 090602 (2004) [arXiv:0311175 [hep-th]].Google Scholar
[262] J., Mas, “Shear viscosity from R-charged AdS black holes,” JHEP 0603, 016 (2006) [arXiv:0601144 [hep-th]].Google Scholar
[263] D. T., Son and A. O., Starinets, “Hydrodynamics of R-charged black holes,” JHEP 0603, 052 (2006) [arXiv:0601157 [hep-th]].Google Scholar
[264] A., Buchel, J. T., Liu and A. O., Starinets, “Coupling constant dependence of the shear viscosity in N = 4 supersymmetric Yang–Mills theory,” Nucl. Phys. B 707, 56 (2005) [arXiv:0406264 [hep-th]].Google Scholar
[265] M., Brigante, H., Liu, R. C., Myers, S., Shenker and S., Yaida, “Viscosity bound violation in higher derivative gravity,” Phys. Rev. D 77, 126006 (2008) [arXiv:0712.0805 [hep-th]].Google Scholar
[266] J., Erdmenger, P., Kerner and H., Zeller, “Non-universal shear viscosity from Einstein gravity,” Phys. Lett. B 699, 301 (2011) [arXiv:1011.5912 [hep-th]].Google Scholar
[267] A., Rebhan and D., Steineder, “Violation of the holographic viscosity bound in a strongly coupled anisotropic plasma,” Phys. Rev. Lett. 108, 021601 (2012) [arXiv:1110.6825 [hep-th]].Google Scholar
[268] J., Polchinski and E., Silverstein, “Large-density field theory, viscosity, and ‘2kF’ singularities from string duals,” Class. Quant. Grav. 29, 194008 (2012) [arXiv:1203.1015 [hep-th]].Google Scholar
[269] M., Brigante, H., Liu, R. C., Myers, S., Shenker and S., Yaida, “The viscosity bound and causality violation,” Phys. Rev. Lett. 100, 191601 (2008) [arXiv:0802.3318 [hep-th]].Google Scholar
[270] R. C., Myers, M. F., Paulos and A., Sinha, “Holographic studies of quasi-topological gravity,” JHEP 1008, 035 (2010) [arXiv:1004.2055 [hep-th]].Google Scholar
[271] S., Jeon and L. G., Yaffe, “From quantum field theory to hydrodynamics: transport coefficients and effective kinetic theory,” Phys. Rev. D 53, 5799 (1996) [arXiv:9512263 [hep-th]].Google Scholar
[272] S. C., Huot, S., Jeon and G. D., Moore, “Shear viscosity in weakly coupled N = 4 super Yang–Mills theory compared to QCD,” Phys. Rev. Lett. 98, 172303 (2007) [arXiv:0608062 [hep-th]].Google Scholar
[273] J., Erlich, “How well does AdS/QCD describe QCD?,” Int. J. Mod. Phys. A 25, 411 (2010) [arXiv:0908.0312 [hep-ph]].Google Scholar
[274] C., Cao, E., Elliott, J., Joseph, H., Wu, J., Petricka, T., Schafer and J. E., Thomas, “Universal quantum viscosity in a unitary Fermi gas,” Science 331, 58 (2010).Google Scholar
[275] T., Schaefer and D., Teaney, “Nearly perfect fluidity: from cold atomic gases to hot quark–gluon plasmas,” Rep. Prog. Phys. 72, 126001 (2009).Google Scholar
[276] P. K., Kovtun and A. O., Starinets, “Quasinormal modes and holography,” Phys. Rev. D 72, 086009 (2005) [arXiv:0506184 [hep-th]].Google Scholar
[277] D. T., Son and A. O., Starinets, “Viscosity, black holes, and quantum field theory,” Ann. Rev. Nucl. Part. Sci. 57, 95 (2007) [arXiv:0704.0240 [hep-th]].Google Scholar
[278] A. Nata, Atmaja and K., Schalm, “Photon and dilepton production in soft wall AdS/QCD,” JHEP 1008, 124 (2010) [arXiv:0802.1460 [hep-th]].Google Scholar
[279] I., Bredberg, C., Keeler, V., Lysov and A., Strominger, “From Navier–Stokes to Einstein” [arXiv:1101.2451 [hep-th]].
[280] K. S., Thorne, R. H., Price and D. A., Macdonald, Black Holes: The Membrane Paradigm, Yale University Press, 1986.
[281] P., Kovtun, “Lectures on hydrodynamic fluctuations in relativistic theories,” J. Phys. A 45, 473001 (2012) [arXiv:1205.5040 [hep-th]].Google Scholar
[282] J., Bhattacharya, S., Bhattacharyya and S., Minwalla, “Dissipative superfluid dynamics from gravity,” JHEP 1104, 125 (2011) [arXiv:1101.3332 [hep-th]].Google Scholar
[283] C. P., Herzog, N., Lisker, P., Surowka and A., Yarom, “Transport in holographic superfluids,” JHEP 1108, 052 (2011) [arXiv:1101.3330 [hep-th]].Google Scholar
[284] J., Bhattacharya, S., Bhattacharyya, S., Minwalla and A., Yarom, “A theory of first order dissipative superfluid dynamics,” JHEP 1405, 147 (2014) [arXiv:1105.3733 [hep-th]].Google Scholar
[285] K., Jensen, M., Kaminski, P., Kovtun, R., Meyer, A., Ritz and A., Yarom, “Parity-violating hydrodynamics in 2 + 1 dimensions,” JHEP 1205, 102 (2012) [arXiv:1112.4498 [hep-th]].Google Scholar
[286] D. T., Son and P., Surowka, “Hydrodynamics with triangle anomalies,” Phys. Rev. Lett. 103, 191601 (2009) [arXiv:0906.5044 [hep-th]].Google Scholar
[287] P. M., Chesler and L. G., Yaffe, “Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang–Mills plasma,” Phys. Rev. Lett. 102, 211601 (2009) [arXiv:0812.2053 [hep-th]].Google Scholar
[288] A., Adams, P. M., Chesler and H., Liu, “Holographic turbulence,” Phys. Rev. Lett. 112, 151602 (2014) [arXiv:1307.7267 [hep-th]].Google Scholar
[289] S., Bhattacharyya, S., Minwalla and S. R., Wadia, “The incompressible nonrelativistic Navier–Stokes equation from gravity,” JHEP 0908, 059 (2009) [arXiv:0810.1545 [hep-th]].Google Scholar
[290] M., Rangamani, “Gravity and hydrodynamics: lectures on the fluid–gravity correspondence,” Class. Quant. Grav. 26, 224003 (2009) [arXiv:0905.4352 [hep-th]].Google Scholar
[291] V. E., Hubeny, S., Minwalla and M., Rangamani, “The fluid/gravity correspondence,” [arXiv:1107.5780 [hep-th]].
[292] J. D., Brown and J.W., York, “Quasilocal energy and conserved charges derived from the gravitational action,” Phys. Rev. D 47, 1407 (1993).Google Scholar
[293] M., Henningson and K., Skenderis, “The holographic Weyl anomaly,” JHEP 9807, 023 (1998) [arXiv:9806087].Google Scholar
[294] V., Juričić, O., Vafek and I. F., Herbut, “Conductivity of interacting massless Dirac particles in graphene: collisionless regime,” Phys. Rev. B 82, 235402 (2010) [arXiv:1009.3269 [cond-mat.mes-hall]].Google Scholar
[295] R. C., Myers, S., Sachdev and A., Singh, “Holographic quantum critical transport without self-duality,” Phys. Rev. D 83, 066017 (2011) [arXiv:1010.0443 [hep-th]].Google Scholar
[296] K., Chen, L., Liu, Y., Deng, L., Pollet and N., Prokof'ev, “Universal conductivity in a two-dimensional superfluid-to-insulator quantum critical system,” Phys. Rev. Lett. 112, 030402 (2013) [arXiv:1309.5635 [cond-mat.str-el]].Google Scholar
[297] D., Chowdhury, S., Raju, S., Sachdev, A., Singh and P, Strack, “Multipoint correlators of conformal field theories: implications for quantum critical transport,” Phys. Rev. B 87, 085138 (2013) [arXiv:1210.5247 [cond-mat.str-el]].Google Scholar
[298] S., Weinberg, The Quantum Theory of Fields. Volume II: Modern Applications, Cambridge University Press, 2001.
[299] D. E., Kharzeev, L. D., McLerran and H. J., Warringa, “The effects of topological charge change in heavy ion collisions: ‘event by event P and CP violation’,” Nucl. Phys. A 803, 227 (2008) [arXiv:0711.0950 [hep-ph]].Google Scholar
[300] K., Fukushima, D. E., Kharzeev and H. J., Warringa, “The chiral magnetic effect,” Phys. Rev. D 78, 074033 (2008) [arXiv:0808.3382 [hep-ph]].Google Scholar
[301] D. E., Kharzeev, “The chiral magnetic effect and anomaly-induced transport,” Prog. Part. Nucl. Phys. 75, 133 (2014) [arXiv:1312.3348 [hep-ph]].Google Scholar
[302] C.-X., Liu, P., Ye and X.-L., Qi, “Chiral gauge field and axial anomaly in a Weyl semi-metal,” Phys. Rev. B 87, 235306 (2013) [arXiv:1204.6551 [cond-mat.str-el]].Google Scholar
[303] D. T., Son and B. Z., Spivak, “Chiral anomaly and classical negative magnetoresistance of Weyl metals,” Phys. Rev. B 88, 104412 (2013), [arXiv:1206.1627 [cond-mat.mes-hall]].Google Scholar
[304] A. A., Zyuzin and A. A., Burkov, “Topological response in Weyl semimetals and the chiral anomaly,” Phys. Rev. B 86, 115133 (2012) [arXiv:1206.1868 [cond-mat. mes-hall]].Google Scholar
[305] K., Landsteiner, “Anomalous transport ofWeyl fermions inWeyl semimetals,” Phys. Rev. B 89, 075124 (2014) [arXiv:1306.4932 [hep-th]].Google Scholar
[306] A. V., Sadofyev and M. V., Isachenkov, “The chiral magnetic effect in hydrodynamical approach,” Phys. Lett. B 697, 404 (2011) [arXiv:1010.1550 [hep-th]].Google Scholar
[307] Y., Neiman and Y., Oz, “Relativistic hydrodynamics with general anomalous charges,” JHEP 1103, 023 (2011) [arXiv:1011.5107 [hep-th]].Google Scholar
[308] V. I., Zakharov, “Chiral magnetic effect in hydrodynamic approximation,” in D., Kharzeev, K., Landsteiner, A., Schmitt and H.-U., Yee (eds), Strongly Interacting Matter in Magnetic Fields, Springer, 2013, p. 295 [arXiv:1210.2186 [hep-ph]].
[309] J., Erdmenger, M., Haack, M., Kaminski and A., Yarom, “Fluid dynamics of Rcharged black holes,” JHEP 0901, 055 (2009) [arXiv:0809.2488 [hep-th]].Google Scholar
[310] N., Banerjee, J., Bhattacharya, S., Bhattacharyya, S., Dutta, R., Loganayagam and P., Surowka, “Hydrodynamics from charged black branes,” JHEP 1101, 094 (2011) [arXiv:0809.2596 [hep-th]].Google Scholar
[311] D. E., Kharzeev, K., Landsteiner, A., Schmitt and H.-U., Yee, “Strongly interacting matter in magnetic fields: an overview,” in D., Kharzeev, K., Landsteiner, A., Schmitt and H.-U., Yee (eds), Strongly Interacting Matter in Magnetic Fields, Springer, 2013, p. 1 [arXiv:1211.6245 [hep-ph]].
[312] O., Saremi and D. T., Son, “Hall viscosity from gauge/gravity duality,” JHEP 1204, 091 (2012) [arXiv:1103.4851 [hep-th]].Google Scholar
[313] D. T., Son and C., Wu, “Holographic spontaneous parity breaking and emergent Hall viscosity and angular momentum,” JHEP 1407, 076 (2014) [arXiv:1311.4882 [hep-th]].Google Scholar
[314] H., Liu, H., Ooguri, B., Stoica and N., Yunes, “Spontaneous generation of angular momentum in holographic theories,” Phys. Rev. Lett. 110, 211601 (2013) [arXiv:1212.3666 [hep-th]].Google Scholar
[315] H., Liu, H., Ooguri and B., Stoica, “Angular momentum generation by parity violation,” Phys. Rev. D 89, 106007 (2014) [arXiv:1311.5879 [hep-th]].Google Scholar
[316] A., Gynther, K., Landsteiner, F., Pena-Benitez and A., Rebhan, “Holographic anomalous conductivities and the chiral magnetic effect,” JHEP 1102, 110 (2011) [arXiv:1005.2587 [hep-th]].Google Scholar
[317] K., Landsteiner, E., Megias and F., Pena-Benitez, “Anomalous transport from Kubo formulae,” in Strongly InteractingMatter inMagnetic Fields, Springer, 2013, p. 433 [arXiv:1207.5808 [hep-th]].
[318] K., Landsteiner, E., Megias and F., Pena-Benitez, “Gravitational anomaly and transport,” Phys. Rev. Lett. 107, 021601 (2011) [arXiv:1103.5006 [hep-ph]].Google Scholar
[319] M., Greiner, O., Mandel, T., Esslinger, T. W., Hänsch and I., Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39 (2002).Google Scholar
[320] T., Faulkner, H., Liu, J., McGreevy and D., Vegh, “Emergent quantum criticality, Fermi surfaces, and AdS2,” Phys. Rev. D 83, 125002 (2011) [arXiv:0907.2694 [hep-th]].Google Scholar
[321] S. S., Gubser and F. D., Rocha, “Peculiar properties of a charged dilatonic black hole in AdS5,” Phys. Rev. D 81, 046001 (2010) [arXiv:0911.2898 [hep-th]].Google Scholar
[322] K., Goldstein, S., Kachru, S., Prakash and S. P., Trivedi, “Holography of charged dilaton black holes,” JHEP 1008, 078 (2010) [arXiv:0911.3586 [hep-th]].Google Scholar
[323] C., Charmousis, B., Gouteraux, B. S., Kim, E., Kiritsis and R., Meyer, “Effective holographic theories for low-temperature condensed matter systems,” JHEP 1011, 151 (2010) [arXiv:1005.4690 [hep-th]].Google Scholar
[324] B., Gouteraux and E., Kiritsis, “Generalized holographic quantum criticality at finite density,” JHEP 1112, 036 (2011) [arXiv:1107.2116 [hep-th]].Google Scholar
[325] M., Edalati, J. I., Jottar and R. G., Leigh, “Holography and the sound of criticality,” JHEP 1010, 058 (2010) [arXiv:1005.4075 [hep-th]].Google Scholar
[326] M., Edalati, J. I., Jottar and R. G., Leigh, “Shear modes, criticality and extremal black holes,” JHEP 1004, 075 (2010) [arXiv:1001.0779 [hep-th]].Google Scholar
[327] R. A., Davison and N. K., Kaplis, “Bosonic excitations of the AdS4 Reissner– Nordström black hole,” JHEP 1112, 037 (2011) [arXiv:1111.0660 [hep-th]].Google Scholar
[328] R. A., Davison and A., Parnachev, “Hydrodynamics of cold holographic matter,” JHEP 1306, 100 (2013) [arXiv:1303.6334 [hep-th]].Google Scholar
[329] C. P., Herzog, “The hydrodynamics of M theory,” JHEP 0212, 026 (2002) [arXiv:0210126 [hep-th]].Google Scholar
[330] C. P., Herzog, “The sound of M theory,” Phys. Rev. D 68, 024013 (2003) [arXiv:0302086 [hep-th]].Google Scholar
[331] L. D., Landau, “Oscillations in a Fermi liquid,” Zh. Éksp. Teor. Fiz. 32, 59 (1957) [Soviet Phys. – JETP 5, 101 (1959)].Google Scholar
[332] M., Edalati, J. I., Jottar and R. G., Leigh, “Transport coefficients at zero temperature from extremal black holes,” JHEP 1001, 018 (2010) [arXiv:0910.0645 [hep-th]].Google Scholar
[333] M., Kaminski, K., Landsteiner, J., Mas, J. P., Shock and J., Tarrio, “Holographic operator mixing and quasinormal modes on the brane,” JHEP 1002, 021 (2010) [arXiv:0911.3610 [hep-th]].Google Scholar
[334] X., Dong, S., Harrison, S., Kachru, G., Torroba and H., Wang, “Aspects of holography for theories with hyperscaling violation,” JHEP 1206, 041 (2012) [arXiv:1201.1905 [hep-th]].Google Scholar
[335] S., Kachru, X., Liu and M., Mulligan, “Gravity duals of Lifshitz-like fixed points,” Phys. Rev. D 78, 106005 (2008) [arXiv:0808.1725 [hep-th]].Google Scholar
[336] L., Huijse, S., Sachdev and B., Swingle, “Hidden Fermi surfaces in compressible states of gauge–gravity duality,” Phys. Rev. B 85, 035121 (2012) [arXiv:1112.0573 [cond-mat.str-el]].Google Scholar
[337] S. S., Gubser and J., Ren, “Analytic fermionic Green's functions from holography,” Phys. Rev. D 86, 046004 (2012) [arXiv:1204.6315 [hep-th]].Google Scholar
[338] M., Spradlin and A., Strominger, “Vacuum states for AdS2 black holes,” JHEP 9911, 021 (1999) [arXiv:9904143 [hep-th]].Google Scholar
[339] A., Almheiri and J., Polchinski, “Models of AdS2 backreaction and holography” [arXiv:1402.6334 [hep-th]].
[340] K., Copsey and R., Mann, “Pathologies in asymptotically Lifshitz spacetimes,” JHEP 1103, 039 (2011) [arXiv:1011.3502 [hep-th]].Google Scholar
[341] G. T., Horowitz and B., Way, “Lifshitz singularities,” Phys. Rev. D 85, 046008 (2012) [arXiv:1111.1243 [hep-th]].Google Scholar
[342] S., Harrison, S., Kachru and H., Wang, “Resolving Lifshitz horizons,” JHEP 1402, 085 (2014) [arXiv:1202.6635 [hep-th]].Google Scholar
[343] N., Bao, X., Dong, S., Harrison and E., Silverstein, “The benefits of stress: resolution of the Lifshitz singularity,” Phys. Rev. D 86, 106008 (2012) [arXiv:1207.0171 [hep-th]].Google Scholar
[344] E., Shaghoulian, “Holographic entanglement entropy and Fermi surfaces,” JHEP 1205, 065 (2012) [arXiv:1112.2702 [hep-th]].Google Scholar
[345] J., Bhattacharya, S., Cremonini and A., Sinkovics, “On the IR completion of geometries with hyperscaling violation,” JHEP 1302, 147 (2013) [arXiv:1208.1752 [hep-th]].Google Scholar
[346] S. A., Hartnoll and E., Shaghoulian, “Spectral weight in holographic scaling geometries,” JHEP 1207, 078 (2012) [arXiv:1203.4236 [hep-th]].Google Scholar
[347] S. S., Gubser, “Breaking an Abelian gauge symmetry near a black hole horizon,” Phys. Rev. D 78, 065034 (2008) [arXiv:0801.2977 [hep-th]].Google Scholar
[348] S. A., Hartnoll, C. P., Herzog and G. T., Horowitz, “Building a holographic superconductor,” Phys. Rev. Lett. 101, 031601 (2008) [arXiv:0803.3295 [hep-th]].Google Scholar
[349] H., Liu, J., McGreevy and D., Vegh, “Non-Fermi liquids from holography,” Phys. Rev. D 83, 065029 (2011) [arXiv:0903.2477 [hep-th]].Google Scholar
[350] M., Cubrovic, J., Zaanen and K., Schalm, “String theory, quantum phase transitions and the emergent Fermi-liquid,” Science 325, 439 (2009) [arXiv:0904.1993 [hep-th]].
[351] S.-S., Lee, “A non-Fermi liquid from a charged black hole: a critical Fermi ball,” Phys. Rev. D 79, 086006 (2009) [arXiv:0809.3402 [hep-th]].Google Scholar
[352] S.-J., Rey, “String theory on thin semiconductors: holographic realization of Fermi points and surfaces,” Prog. Theor. Phys. Suppl. 177, 128 (2009) [arXiv:0911.5295 [hep-th]].Google Scholar
[353] V., Juričić;, I. F., Herbut and G. W., Semenoff, “Coulomb interaction at the metal–insulator critical point in graphene,” Phys. Rev. B 80, 081405 (2009) [arXiv:0906.3513 [cond-mat.str-el]].Google Scholar
[354] R., Contino and A., Pomarol, “Holography for fermions,” JHEP 0411, 058 (2004) [arXiv:0406257 [hep-th]].Google Scholar
[355] J. P., Gauntlett, J., Sonner and D., Waldram, “Universal fermionic spectral functions from string theory,” Phys. Rev. Lett. 107, 241601 (2011) [arXiv:1106.4694 [hep-th]].Google Scholar
[356] T., Faulkner, N., Iqbal, H., Liu, J., McGreevy and D., Vegh, “Holographic non-Fermi liquid fixed points,” Phil. Trans. Roy. Soc. A 369, 1640 (2011) [arXiv:1101.0597 [hep-th]].Google Scholar
[357] M., Cubrovic, Y., Liu, K., Schalm, Y.-W., Sun and J., Zaanen, “Spectral probes of the holographic Fermi groundstate: dialing between the electron star and AdS Dirac hair,” Phys. Rev. D 84, 086002 (2011) [arXiv:1106.1798 [hep-th]].Google Scholar
[358] B., Pioline and J., Troost, “Schwinger pair production in AdS2,” JHEP 0503, 043 (2005) [arXiv:0501169 [hep-th]].Google Scholar
[359] Y., Liu, K., Schalm, Y. W., Sun and J., Zaanen, “Lattice potentials and fermions in holographic non Fermi-liquids: hybridizing local quantum criticality,” JHEP 1210, 036 (2012) [arXiv:1205.5227 [hep-th]].Google Scholar
[360] T., Hartman and S. A., Hartnoll, “Cooper pairing near charged black holes,” JHEP 1006, 005 (2010) [arXiv:1003.1918 [hep-th]].Google Scholar
[361] T., Faulkner, N., Iqbal, H., Liu, J., McGreevy and D., Vegh, “Strange metal transport realized by gauge/gravity duality,” Science 329, 1043 (2010).Google Scholar
[362] O., DeWolfe, S. S., Gubser and C., Rosen, “Fermi surfaces in maximal gauged supergravity,” Phys. Rev. Lett. 108, 251601 (2012) [arXiv:1112.3036 [hep-th]].Google Scholar
[363] O., DeWolfe, S. S., Gubser and C., Rosen, “Fermi surfaces in N = 4 super-Yang– Mills theory,” Phys. Rev. D 86, 106002 (2012) [arXiv:1207.3352 [hep-th]].Google Scholar
[364] T., Faulkner, N., Iqbal, H., Liu, J., McGreevy and D., Vegh, “From black holes to strange metals” [arXiv:1003.1728 [hep-th]].
[365] J., Polchinski, “Low energy dynamics of the spinon–gauge system,” Nucl. Phys. B 422, 617 (1994). [arXiv:9303037 [cond-mat]].Google Scholar
[366] T., Faulkner and J., Polchinski, “Semi-holographic Fermi liquids,” JHEP 1106, 012 (2011) [arXiv:1001.5049 [hep-th]].Google Scholar
[367] S. A., Hartnoll, C. P., Herzog and G. T., Horowitz, “Holographic superconductors,” JHEP 0812, 015 (2008) [arXiv:0810.1563 [hep-th]].Google Scholar
[368] R., Ruffini and J. A., Wheeler, “Introducing the black hole,” Physics Today 24, 30 (1971).Google Scholar
[369] D., Anninos, S. A., Hartnoll and N., Iqbal, “Holography and the Coleman–Mermin– Wagner theorem,” Phys. Rev. D 82, 066008 (2010) [arXiv:1005.1973 [hep-th]].Google Scholar
[370] M., Ammon, J., Erdmenger, M., Kaminski and P., Kerner, “Superconductivity from gauge/gravity duality with flavor,” Phys. Lett. B 680, 516 (2009) [arXiv:0810.2316 [hep-th]].Google Scholar
[371] T., Albash and C. V., Johnson, “Vortex and droplet engineering in holographic superconductors,” Phys. Rev. D 80, 126009 (2009) [arXiv:0906.1795 [hep-th]].Google Scholar
[372] M., Montull, A., Pomarol and P. J., Silva, “The holographic superconductor vortex,” Phys. Rev. Lett. 103, 091601 (2009) [arXiv:0906.2396 [hep-th]].Google Scholar
[373] K., Maeda, M., Natsuume and T., Okamura, “Vortex lattice for a holographic superconductor,” Phys. Rev. D 81, 026002 (2010) [arXiv:0910.4475 [hep-th]].Google Scholar
[374] V., Keranen, E., Keski-Vakkuri, S., Nowling and K. P., Yogendran, “Inhomogeneous structures in holographic superfluids: I. Dark solitons,” Phys. Rev. D 81, 126011 (2010) [arXiv:0911.1866 [hep-th]].Google Scholar
[375] A., Adams, P. M., Chesler and H., Liu, “Holographic vortex liquids and superfluid turbulence,” Science 341, 368 (2013) [arXiv:1212.0281 [hep-th]].Google Scholar
[376] L. D., Landau, “Theory of the superfluidity of helium II,” Phys. Rev. 60, 356 (1941).Google Scholar
[377] L., Tisza, “The theory of liquid helium,” Phys. Rev. 72, 838 (1947).
[378] W., Israel, “Covariant superfluid mechanics,” Phys. Lett. A 86, 79 (1981).
[379] I., M.|Khalatnikov and V. V., Lebedev, “Second sound in liquid helium II,” Phys. Lett. A 91, 70 (1982).Google Scholar
[380] W., Israel, “Equivalence of two theories of relativistic superfluid mechanics,” Phys. Lett. A 92, 77 (1982).Google Scholar
[381] D., T. Son, “Hydrodynamics of relativistic systems with broken continuous symmetries,” Int. J. Mod. Phys. A 16 (suppl. 01C), 1284 (2001) [arXiv:0011246 [hep-th]].Google Scholar
[382] J., Sonner and B., Withers, “A gravity derivation of the Tisza–Landau model in AdS/CFT,” Phys. Rev. D 82, 026001 (2010) [arXiv:1004.2707 [hep-th]].
[383] G., T. Horowitz, J. E., Santos and B., Way, “A holographic Josephson junction,” Phys. Rev. Lett. 106, 221601 (2011) [arXiv:1101.3326 [hep-th]].Google Scholar
[384] E., Kiritsis and V., Niarchos, “Josephson junctions and AdS/CFT networks,” JHEP 1107, 112 (2011) [Erratum ibid. 1110, 095 (2011)] [arXiv:1105.6100 [hep-th]].Google Scholar
[385] T., Faulkner, G. T., Horowitz, J., McGreevy, M. M., Roberts and D., Vegh, “Photoemission ‘experiments’ on holographic superconductors,” JHEP 1003, 121 (2010) [arXiv:0911.3402 [hep-th]].Google Scholar
[386] J.-W., Chen, Y.-J., Kao and W.-Y., Wen, “Peak–dip–hump from holographic superconductivity,” Phys. Rev. D 82, 026007 (2010) [arXiv:0911.2821 [hep-th]].Google Scholar
[387] S. S., Gubser and S. S., Pufu, “The gravity dual of a p-wave superconductor,” JHEP 0811, 033 (2008) [arXiv:0805.2960 [hep-th]].Google Scholar
[388] M. M., Roberts and S. A., Hartnoll, “Pseudogap and time reversal breaking in a holographic superconductor,” JHEP 0808, 035 (2008) [arXiv:0805.3898 [hep-th]].Google Scholar
[389] F., Benini, C. P., Herzog and A., Yarom, “Holographic Fermi arcs and a d-wave gap,” Phys. Lett. B 701, 626 (2011) [arXiv:1006.0731 [hep-th]].Google Scholar
[390] F., Benini, C. P., Herzog, R., Rahman and A., Yarom, “Gauge gravity duality for d-wave superconductors: prospects and challenges,” JHEP 1011, 137 (2010) [arXiv:1007.1981 [hep-th]].Google Scholar
[391] K., Y. Kim and M., Taylor, “Holographic d-wave superconductors,” JHEP 1308, 112 (2013) [arXiv:1304.6729 [hep-th]].Google Scholar
[392] M., Ammon, J., Erdmenger, V., Grass, P., Kerner and A., O'Bannon, “On holographic p-wave superfluids with back-reaction,” Phys. Lett. B 686, 192 (2010) [arXiv:0912.3515 [hep-th]].Google Scholar
[393] S., S. Gubser, F. D., Rocha and A., Yarom, “Fermion correlators in non-Abelian holographic superconductors,” JHEP 1011, 085 (2010) [arXiv:1002.4416 [hep-th]].Google Scholar
[394] J., Erdmenger, D., Fernandez and H., Zeller, “New transport properties of anisotropic holographic superfluids,” JHEP 1304, 049 (2013) [arXiv:1212.4838 [hep-th]].Google Scholar
[395] R. A., Ferrell, “Fluctuations and the superconducting phase transition: II. Onset of Josephson tunneling and paraconductivity of a junction,” J. Low Temp. Phys. 1, 423 (1969).Google Scholar
[396] D. J., Scalapino, “Pair tunneling as a probe of fluctuations in superconductors,” Phys. Rev. Lett. 24, 1052 (1970).Google Scholar
[397] J. T., Anderson and A. M., Goldman, “Experimental determination of the pair susceptibility of a superconductor,” Phys. Rev. Lett. 25, 743 (1970).Google Scholar
[398] A. M., Goldman, “The order parameter susceptibility and collective modes of superconductors,” J. Supercond. Nov. Magn. 19, 317 (2006).Google Scholar
[399] A. V., Chubukov, D., Pines and J., Schmalian, “Spin fluctuation model for d-wave superconductivity,” in K. H., Bennemann and J. B., Ketterson(eds), The Physics of Superconductors, Vol. 1, Springer, 2004, pp. 495–590.
[400] K., Jensen, “Semi-holographic quantum criticality,” Phys. Rev. Lett. 107, 231601 (2011) [arXiv:1108.0421 [hep-th]].Google Scholar
[401] D. B., Kaplan, J.-W., Lee, D. T., Son and M. A., Stephanov, “Conformality lost,” Phys. Rev. D 80, 125005 (2009) [arXiv:0905.4752 [hep-th]].Google Scholar
[402] T., Nishioka, S., Ryu and T., Takayanagi, “Holographic superconductor/insulator transition at zero temperature,” JHEP 1003, 131 (2010) [arXiv:0911.0962 [hep-th]].Google Scholar
[403] G. T., Horowitz and B., Way, “Complete phase diagrams for a holographic superconductor/insulator system,” JHEP 1011, 011 (2010) [arXiv:1007.3714 [hep-th]].Google Scholar
[404] S. S., Gubser and A., Nellore, “Ground states of holographic superconductors,” Phys. Rev. D 80, 105007 (2009) [arXiv:0908.1972 [hep-th]].Google Scholar
[405] G. T., Horowitz and M. M., Roberts, “Zero temperature limit of holographic superconductors,” JHEP 0911, 015 (2009) [arXiv:0908.3677 [hep-th]].Google Scholar
[406] N., Iqbal, H., Liu, M., Mezei and Q., Si, “Quantum phase transitions in holographic models of magnetism and superconductors,” Phys. Rev. D 82, 045002 (2010) [arXiv:1003.0010 [hep-th]].Google Scholar
[407] P. W., Anderson, “In praise of unstable fixed points: the way things actually work,” Physica B: Condensed Matter 318, 28 (2002) [arXiv:0201431 [cond-mat]].Google Scholar
[408] P. C., W. Davies, “Thermodynamics of black holes,” Rep. Prog. Phys. 41, 1313 (1978).Google Scholar
[409] M. V., Medvedyeva, E., Gubankova, M., Cubrovic, K., Schalm and J., Zaanen, “Quantum corrected phase diagram of holographic fermions,” JHEP 1312, 025 (2013) [arXiv:1302.5149 [hep-th]].Google Scholar
[410] S. A., Hartnoll and P., Petrov, “Electron star birth: a continuous phase transition at nonzero density,” Phys. Rev. Lett. 106, 121601 (2011) [arXiv:1011.6469 [hep-th]].Google Scholar
[411] V. G., M. Puletti, S., Nowling, L., Thorlacius and T., Zingg, “Holographic metals at finite temperature,” JHEP 1101, 117 (2011) [arXiv:1011.6261 [hep-th]].Google Scholar
[412] A., Allais, J., McGreevy and S. J., Suh, “A quantum electron star,” Phys. Rev. Lett. 108, 231602 (2012) [arXiv:1202.5308 [hep-th]].Google Scholar
[413] A., Allais and J., McGreevy, “How to construct a gravitating quantum electron star,” Phys. Rev. D 88, 066006 (2013) [arXiv:1306.6075 [hep-th]].Google Scholar
[414] S., Sachdev, “A model of a Fermi liquid using gauge–gravity duality,” Phys. Rev. D 84, 066009 (2011) [arXiv:1107.5321 [hep-th]].Google Scholar
[415] E., Witten, “Baryons in the 1/N expansion,” Nucl. Phys. B 160, 57 (1979).Google Scholar
[416] E., Witten, “Baryons and branes in anti-de Sitter space,” JHEP 9807, 006 (1998) [arXir:9805112 [hep-th]].Google Scholar
[417] C. P., Herzog and J., Ren, “The spin of holographic electrons at nonzero density and temperature,” JHEP 1206, 078 (2012) [arXiv:1204.0518 [hep-th]].Google Scholar
[418] S. A., Hartnoll and A., Tavanfar, “Electron stars for holographic metallic criticality,” Phys. Rev. D 83, 046003 (2011) [arXiv:1008.2828 [hep-th]].Google Scholar
[419] N., Iizuka, N., Kundu, P., Narayan and S. P., Trivedi, “Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity,” JHEP 1201, 094 (2012) [arXiv:1105.1162 [hep-th]].Google Scholar
[420] S., A. Hartnoll, D. M., Hofman and D., Vegh, “Stellar spectroscopy: fermions and holographic Lifshitz criticality,” JHEP 1108, 096 (2011) [arXiv:1105.3197 [hep-th]].Google Scholar
[421] N., Iqbal and H., Liu, “Luttinger's theorem, superfluid vortices, and holography,” Class. Quant. Grav. 29, 194004 (2012) [arXiv:1112.3671 [hep-th]].Google Scholar
[422] S., A. Hartnoll and L., Huijse, “Fractionalization of holographic Fermi surfaces,” Class. Quant. Grav. 29, 194001 (2012) [arXiv:1111.2606 [hep-th]].Google Scholar
[423] M., Cubrovic, K., Schalm and J., Zaanen, “The quantum phase transition from an AdS Reissner–Nordström black hole to an AdS electron star” (to be published).
[424] D., J. Gross and E., Witten, “Possible third order phase transition in the large-N lattice gauge theory,” Phys. Rev. D 21, 446 (1980).Google Scholar
[425] A., Bagrov, B., Meszena and K., Schalm, “Pairing induced superconductivity in holography,” JHEP 1409, 106 (2014) [arXiv:1403.3699 [hep-th]].Google Scholar
[426] Y., Liu, K., Schalm, Y. W., Sun and J., Zaanen, “BCS instabilities of electron stars to holographic superconductors,” JHEP 1405, 122 (2014) [arXiv:1404.0571 [hep-th]].Google Scholar
[427] J., de Boer, K., Papadodimas and E., Verlinde, “Holographic neutron stars,” JHEP 1010, 020 (2010) [arXiv:0907.2695 [hep-th]].Google Scholar
[428] X., Arsiwalla, J. de, Boer, K., Papadodimas and E., Verlinde, “Degenerate stars and gravitational collapse in AdS/CFT,” JHEP 1101, 144 (2011) [arXiv:1010.5784 [hep-th]].Google Scholar
[429] J. M., Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids, Oxford University Press, 1960.
[430] W. E., Lawrence and J. W., Wilkins, “Electron–electron scattering in the transport coefficients of simple metals,” Phys. Rev. B 7, 2317 (1973).Google Scholar
[431] W., Götze and P., Wölfle, “Homogeneous dynamical conductivity of simple metals,” Phys. Rev. B 6, 1226 (1972).Google Scholar
[432] A., Rosch and N., Andrei, “Conductivity of a clean one-dimensional wire,” Phys. Rev. Lett. 85, 1092 (2000).Google Scholar
[433] S., A. Hartnoll and D. M., Hofman, “Locally critical resistivities from umklapp scattering,” Phys. Rev. Lett. 108, 241601 (2012) [arXiv:1201.3917 [hep-th]].Google Scholar
[434] R., Mahajan, M., Barkeshli and S. A., Hartnoll, “Non-Fermi liquids and the Wiedemann–Franz law,” Phys. Rev. B 88, 125107 (2013) [arXiv:1304.4249 [condmat. str-el]].Google Scholar
[435] A., V. Andreev, S. A., Kivelson and B., Spivak, “Hydrodynamic description of transport in strongly correlated electron systems,” Phys. Rev. Lett. 106, 256804 (2011).Google Scholar
[436] M., Blake, D., Tong and D., Vegh, “Holographic lattices give the graviton a mass,” Phys. Rev. Lett. 112, 071602 (2014) [arXiv:1310.3832 [hep-th]].Google Scholar
[437] R., Flauger, E., Pajer and S., Papanikolaou, “A striped holographic superconductor,” Phys. Rev. D 83, 064009 (2011) [arXiv:1010.1775 [hep-th]].Google Scholar
[438] G. T., Horowitz, J. E., Santos and D., Tong, “Optical conductivity with holographic lattices,” JHEP 1207, 168 (2012) [arXiv:1204.0519 [hep-th]].Google Scholar
[439] G. T., Horowitz, J. E., Santos and D., Tong, “Further evidence for lattice-induced scaling,” JHEP 1211, 102 (2012) [arXiv:1209.1098 [hep-th]].Google Scholar
[440] G. T., Horowitz and J. E., Santos, “General relativity and the cuprates,” JHEP 1306, 087 (2013) [arXiv:1302.6586 [hep-th]].Google Scholar
[441] D., van der Marel, H. J. A., Molegraaf, J., Zaanen, Z., Nussinov, F., Carbone, A., Damascelli, H., Eisaki, M., Greven, P. H., Kes and M., Li, “Quantum critical behaviour in a high-Tc superconductor,” Nature 425, 271 (2003) [arXiv:0309172 [cond-mat.str-el]].Google Scholar
[442] D., Dalidovich and P., Phillips, “Nonlinear transport near a quantum phase transition in two dimensions,” Phys. Rev. Lett. 93, 27004 (2004) [arXiv:0310129 [cond-mat.supr-con]].Google Scholar
[443] D. A., Bonn, R., Liang, T. M., Riseman, D. J., Baar, D. C., Morgan, K., Zhang, P., Dosanjh, T. L., Duty, A., MacFarlane, G. D., Morris, J. H., Brewer, W. N., Hardy, C., Kallin and A. J., Berlinsky, “Microwave determination of the quasiparticle scattering time in YBa2Cu3O6.95,” Phys. Rev. B 47, 11314 (1993).Google Scholar
[444] J., Orenstein, “Optical conductivity and spatial inhomogeneity in cuprate superconductors,” in Handbook of High-Temperature Superconductivity. Theory and Experiment, Springer, 2007.
[445] M., P. Ryan and L. C., Shepley, Homogeneous Relativistic Cosmologies, Princeton University Press, 1975.
[446] N., Iizuka, S., Kachru, N., Kundu, P., Narayan, N., Sircar and S. P., Trivedi, “Bianchi attractors: a classification of extremal black brane geometries,” JHEP 1207, 193 (2012) [arXiv:1201.4861 [hep-th]].Google Scholar
[447] A., Donos and S. A., Hartnoll, “Interaction-driven localization in holography,” Nature Physics 9, 649 (2013) [arXiv:1212.2998].Google Scholar
[448] E., D'Hoker and P., Kraus, “Charge expulsion from black brane horizons, and holographic quantum criticality in the plane,” JHEP 1209, 105 (2012) [arXiv:1202.2085 [hep-th]].Google Scholar
[449] J., Zaanen, “High-temperature superconductivity: the secret of the hourglass,” Nature 471, 314 (2011).Google Scholar
[450] V. J., Emery, E., Fradkin, S. A., Kivelson and T. C., Lubensky, “Quantum theory of the smectic metal state in stripe phases,” Phys. Rev. Lett. 85, 2160 (2000) [arXiv:condmat/ 0001077 [cond-mat.str-el]].Google Scholar
[451] G. T., Horowitz and M. M., Roberts, “Holographic superconductors with various condensates,” Phys. Rev. D 78, 126008 (2008) [arXiv:0810.1077 [hep-th]].Google Scholar
[452] M., Taylor, “More on counterterms in the gravitational action and anomalies” [arXiv:0002125 [hep-th]].
[453] A., Donos and J. P., Gauntlett, “Holographic Q-lattices,” JHEP 1404, 040 (2014) [arXiv:1311.3292 [hep-th]].Google Scholar
[454] A., Donos and J. P., Gauntlett, “Novel metals and insulators from holography,” JHEP 1406, 007 (2014) [arXiv:1401.5077 [hep-th]].Google Scholar
[455] T., Andrade and B., Withers, “A simple holographic model of momentum relaxation,” JHEP 1405, 101 (2014) [arXiv:1311.5157 [hep-th]].Google Scholar
[456] B., Gouteraux, “Charge transport in holography with momentum dissipation,” JHEP 1404, 181 (2014) [arXiv:1401.5436 [hep-th]].Google Scholar
[457] K., Hinterbichler, “Theoretical aspects of massive gravity,” Rev. Mod. Phys. 84, 671 (2012) [arXiv:1105.3735 [hep-th]].Google Scholar
[458] C., de Rham, “Massive gravity,” Living Rev. Rel. 17, 7 (2014) [arXiv:1401.4173 [hep-th]].Google Scholar
[459] C., de Rham, G., Gabadadze and A. J., Tolley, “Resummation of massive gravity,” Phys. Rev. Lett. 106, 231101 (2011) [arXiv:1011.1232 [hep-th]].Google Scholar
[460] H., Kleinert, Gauge Fields in Condensed Matter. Volume 2: Stresses and Defects. Differential Geometry, Crystal Melting, World Scientific, 1989.Google Scholar
[461] H., Kleinert, Multivalued Fields in Condensed Matter, Electromagnetism, and Gravitation, World Scientific, 2008.Google Scholar
[462] L., Giomi and M., Bowick, “Two-dimensional matter: order, curvature and defects,” Adv. Phys. 58, 449 (2009) [arXiv:0812.3064 [cond-mat.soft]].Google Scholar
[463] A. J., Beekman, K., Wu, V., Cvetkovic and J., Zaanen, “Deconfining the rotational Goldstone mode: the superconducting nematic liquid crystal in 2 +1D,” Phys. Rev. B 88, 024121 (2013) [arXiv:1301.7329 [cond-mat.str-el]].Google Scholar
[464] J., Zaanen and A. J., Beekman, “The emergence of gauge invariance: the stayat- home gauge versus local-global duality,” Annals of Physics 327, 1146 (2012) [arXiv:1108.2791 [cond-mat.str-el]].Google Scholar
[465] D., Vegh, “Holography without translational symmetry” [arXiv:1301.0537 [hep-th]].
[466] M., Blake and D., Tong, “Universal resistivity from holographic massive gravity,” Phys. Rev. D 88, 106004 (2013) [arXiv:1308.4970 [hep-th]].Google Scholar
[467] R. A., Davison, “Momentum relaxation in holographic massive gravity,” Phys. Rev. D 88, 086003 (2013) [arXiv:1306.5792 [hep-th]].Google Scholar
[468] R. A., Davison, K., Schalm and J., Zaanen, “Holographic duality and the resistivity of strange metals,” Phys. Rev. B 89, 245116 (2014) [arXiv:1311.2451 [hep-th]].Google Scholar
[469] J. A., N. Bruin, H., Sakai, R. S., Perry and A. P., Mackenzie, “Similarity of scattering rates in metals showing T -linear resistivity,” Science 339, 804 (2013).Google Scholar
[470] A., Lucas, S., Sachdev and K., Schalm, “Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder,” Phys. Rev. D 89, 066018 (2014) [arXiv:1401.7993 [hep-th]].Google Scholar
[471] B., Bradlyn, M., Goldstein and N., Read, “Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity,” Phys. Rev. B 86, 245309 (2012) [arXiv:1207.7021 [cond-mat.stat-mech]].Google Scholar
[472] S., Sachdev and J.W., Ye, “Universal quantum critical dynamics of two-dimensional antiferromagnets,” Phys. Rev. Lett. 69, 2411 (1992) [arXiv:9204001 [cond-mat]].Google Scholar
[473] S., Sachdev, “Universal relaxational dynamics near two-dimensional quantum critical points,” Phys. Rev. B 59, 14054 (1999) [arXiv:9810399 [cond-mat.str-el]].Google Scholar
[474] S., A. Hartnoll, R., Mahajan, M., Punk and S., Sachdev, “Transport near the Isingnematic quantum critical point of metals in two dimensions,” Phys. Rev. B 89, 155130 (2014) [arXiv:1401.7012 [cond-mat.str-el]].Google Scholar
[475] S., Nakamura, H., Ooguri and C.-S., Park, “Gravity dual of spatially modulated phase,” Phys. Rev. D 81, 044018 (2010) [arXiv:0911.0679 [hep-th]].Google Scholar
[476] H., Ooguri and C.-S., Park, “Holographic end-point of spatially modulated phase transition,” Phys. Rev. D 82, 126001 (2010) [arXiv:1007.3737 [hep-th]].Google Scholar
[477] A., Donos and J. P., Gauntlett, “Holographic striped phases,” JHEP 1108, 140 (2011) [arXiv:1106.2004 [hep-th]].Google Scholar
[478] O., Bergman, N., Jokela, G., Lifschytz and M., Lippert, “Striped instability of a holographic Fermi-like liquid,” JHEP 1110, 034 (2011) [arXiv:1106.3883 [hep-th]].Google Scholar
[479] S., Chakravarty, R. B., Laughlin, D. K., Morr and C., Nayak, “Hidden order in the cuprates,” Phys. Rev. B 63, 094503 (2001).Google Scholar
[480] P. A., Lee, N., Nagaosa and X.-G., Wen, “Doping a Mott insulator: physics of hightemperature superconductivity,” Rev. Mod. Phys. 78, 17 (2006).Google Scholar
[481] A., Shekhter and C. M., Varma, “Considerations on the symmetry of loop order in cuprates,” Phys. Rev. B 80, 214501 (2009) [arXiv:0905.1987 [cond-mat.supr-con]].Google Scholar
[482] A., Allais, J., Bauer and S., Sachdev, “Bond order instabilities in a correlated two-dimensional metal,” Phys. Rev. B 90, 155114 (2014) [arXiv:1402.4807 [condmat. str-el]].Google Scholar
[483] A., Donos and J. P., Gauntlett, “Holographic charge density waves,” Phys. Rev. D 87, 126008 (2013) [arXiv:1303.4398 [hep-th]].Google Scholar
[484] A., Donos and J. P., Gauntlett, “Black holes dual to helical current phases,” Phys. Rev. D 86, 064010 (2012) [arXiv:1204.1734 [hep-th]].Google Scholar
[485] J., P. Gauntlett, S., Kim, O., Varela and D., Waldram, “Consistent supersymmetric Kaluza–Klein truncations with massive modes,” JHEP 0904, 102 (2009) [arXiv:0901.0676 [hep-th]].Google Scholar
[486] M., Rozali, D., Smyth, E., Sorkin and J. B., Stang, “Holographic stripes,” Phys. Rev. Lett. 110, 201603 (2013) [arXiv:1211.5600 [hep-th]].Google Scholar
[487] A., Donos, “Striped phases from holography,” JHEP 1305, 059 (2013) [arXiv:1303.7211 [hep-th]].Google Scholar
[488] B., Withers, “Black branes dual to striped phases,” Class. Quant. Grav. 30, 155025 (2013) [arXiv:1304.0129 [hep-th]].Google Scholar
[489] M., Rozali, D., Smyth, E., Sorkin and J. B., Stang, “Striped order in AdS/CFT correspondence,” Phys. Rev. D 87, 126007 (2013) [arXiv:1304.3130 [hep-th]].Google Scholar
[490] A., Karch and E., Katz, “Adding flavor to AdS/CFT,” JHEP 0206, 043 (2002) [arXiv:0205236 [hep-th]].Google Scholar
[491] L. E., Ibanez and A. M., Uranga, String Theory and Particle Physics: An Introduction to String Phenomenology, Cambridge University Press, 2012.
[492] P. S., Aspinwall, “Compactification, Geometry and Duality: N = 2,” TASI 1999 Lectures, report DUKE-CGTP-00-01 [arXiv:0001001 [hep-th]].
[493] F., Denef and S. A., Hartnoll, “Landscape of superconducting membranes,” Phys. Rev. D 79, 126008 (2009) [arXiv:0901.1160 [hep-th]].Google Scholar
[494] J. P., Gauntlett, J., Sonner and T., Wiseman, “Holographic superconductivity in Mtheory,” Phys. Rev. Lett. 103, 151601 (2009) [arXiv:0907.3796 [hep-th]].Google Scholar
[495] J. P., Gauntlett, J., Sonner and T., Wiseman, “Quantum criticality and holographic superconductors in M-theory,” JHEP 1002, 060 (2010) [arXiv:0912.0512 [hep-th]].Google Scholar
[496] M. J., Duff and J. T., Liu, “Anti-de Sitter black holes in gauged N = 8 supergravity,” Nucl. Phys. B 554, 237 (1999) [arXiv:9901149 [hep-th]].Google Scholar
[497] S. S., Gubser and I., Mitra, “The evolution of unstable black holes in anti-de Sitter space,” JHEP 0108, 018 (2001) [arXiv:0011127 [hep-th]].Google Scholar
[498] R. C., Myers, “Dielectric branes,” JHEP 9912, 022 (1999) [arXiv:9910053 [hep-th]].Google Scholar
[499] M., Born and L., Infeld, “Foundations of the new field theory,” Proc. R. Soc. Lond. A 144, 425 (1934).Google Scholar
[500] P. A. M., Dirac, “A reformulation of the Born–Infeld electrodynamics,” Proc. R. Soc. A 257, 32 (1960).Google Scholar
[501] R. G., Leigh, “Dirac–Born–Infeld action from Dirichlet sigma model,” Mod. Phys. Lett. A 4, 2767 (1989).Google Scholar
[502] A. A., Tseytlin, “On non-Abelian generalization of Born–Infeld action in string theory,” Nucl. Phys. B 501, 41 (1997) [arXiv:9701125 [hep-th]].Google Scholar
[503] A. A., Tseytlin, “Born–Infeld action, supersymmetry and string theory,” in M. A., Shifman (ed.), The Many Faces of the Superworld, World Scientific, 2000, pp. 417–452 [arXiv:9908105 [hep-th]].
[504] S., Kobayashi, D., Mateos, S., Matsuura, R. C., Myers and R. M., Thomson, “Holographic phase transitions at finite baryon density,” JHEP 0702, 016 (2007) [arXiv:0611099 [hep-th]].Google Scholar
[505] A., Karch and A., O'Bannon, “Metallic AdS/CFT,” JHEP 0709, 024 (2007) [arXiv:0705.3870 [hep-th]].Google Scholar
[506] J., Erdmenger, N., Evans, I., Kirsch and E., Threlfall, “Mesons in gauge/gravity duals – a review,” Eur. Phys. J. A 35, 81 (2008) [arXiv:0711.4467 [hep-th]].Google Scholar
[507] A., O'Bannon, “Holographic thermodynamics and transport of flavor fields” [arXiv:0808.1115 [hep-th]].
[508] S. A., Hartnoll, J., Polchinski, E., Silverstein and D., Tong, “Towards strange metallic holography,” JHEP 1004, 120 (2010) [arXiv:0912.1061 [hep-th]].Google Scholar
[509] A., O'Bannon, “Hall conductivity of flavor fields from AdS/CFT,” Phys. Rev. D 76, 086007 (2007) [arXiv:0708.1994 [hep-th]].Google Scholar
[510] O., Bergman, J., Erdmenger and G., Lifschytz, “A review of magnetic phenomena in probe-brane holographic matter,” in D., Kharzeev, K., Landsteiner, A., Schmitt and H.-U., Yee (eds), Strongly Interacting Matter in Magnetic Fields, Springer, 2013, p. 591 [arXiv:1207.5953 [hep-th]].
[511] M., Ammon, J., Erdmenger, M., Kaminski and P., Kerner, “Flavor superconductivity from gauge/gravity duality,” JHEP 0910, 067 (2009) [arXiv:0903.1864 [hep-th]].Google Scholar
[512] S., Harrison, S., Kachru and G., Torroba, “A maximally supersymmetric Kondo model,” Class. Quant. Grav. 29, 194005 (2012) [arXiv:1110.5325 [hep-th]].Google Scholar
[513] J., Erdmenger, C., Hoyos, A., Obannon and J., Wu, “A holographic model of the Kondo effect,” JHEP 1312, 086 (2013) [arXiv:1310.3271 [hep-th]].Google Scholar
[514] A. W. W., Ludwig, “Field theory approach to critical quantum impurity problems and applications to the multichannel Kondo effect,” Int. J. Mod. Phys. B 8, 347 (1994).Google Scholar
[515] I., Affleck, “Conformal field theory approach to the Kondo effect,” Acta Phys. Polon. B 26, 1869 (1995) [arXiv:9512099 [cond-mat]].Google Scholar
[516] S., Kachru, A., Karch and S., Yaida, “Adventures in holographic dimer models,” New J. Phys. 13, 035004 (2011) [arXiv:1009.3268 [hep-th]].Google Scholar
[517] A., Kolezhuk, S., Sachdev, R. R., Biswas and P., Chen, “Theory of quantum impurities in spin liquids,” Phys. Rev. B 74, 165114 (2006) [arXiv:0606385 [cond-mat]].Google Scholar
[518] J., L. Davis, P., Kraus and A., Shah, “Gravity dual of a quantum Hall plateau transition,” JHEP 0811, 020 (2008) [arXiv:0809.1876 [hep-th]].Google Scholar
[519] M., Fujita, W., Li, S., Ryu and T., Takayanagi, “Fractional quantum Hall effect via holography: Chern–Simons, edge states, and hierarchy,” JHEP 0906, 066 (2009) [arXiv:0901.0924 [hep-th]].Google Scholar
[520] O., Bergman, N., Jokela, G., Lifschytz and M., Lippert, “Quantum Hall effect in a holographic model,” JHEP 1010, 063 (2010) [arXiv:1003.4965 [hep-th]].Google Scholar
[521] S., Kachru, A., Karch and S., Yaida, “Holographic lattices, dimers, and glasses,” Phys. Rev. D 81, 026007 (2010) [arXiv:0909.2639 [hep-th]].Google Scholar
[522] A., Karch, D. T., Son and A. O., Starinets, “Zero sound from holography,” Phys. Rev. Lett. 102, 051602 (2009) [arXiv:0806.3796 [hep-th]].Google Scholar
[523] M., Kulaxizi and A., Parnachev, “Comments on Fermi liquid from holography,” Phys. Rev. D 78, 086004 (2008) [arXiv:0808.3953 [hep-th]].Google Scholar
[524] R. A., Davison and A. O., Starinets, “Holographic zero sound at finite temperature,” Phys. Rev. D 85, 026004 (2012) [arXiv:1109.6343 [hep-th]].Google Scholar
[525] Y. Y., Bu, J., Erdmenger, J. P., Shock and M., Strydom, “Magnetic field induced lattice ground states from holography,” JHEP 1303, 165 (2013) [arXiv:1210.6669 [hep-th]].Google Scholar
[526] K., Jensen, A., Karch, D. T., Son and E. G., Thompson, “Holographic Berezinskii–Kosterlitz–Thouless transitions,” Phys. Rev. Lett. 105, 041601 (2010) [arXiv:1002.3159 [hep-th]].Google Scholar
[527] S., Ryu and T., Takayanagi, “Topological insulators and superconductors from Dbranes,” Phys. Lett. B 693, 175 (2010) [arXiv:1001.0763 [hep-th]].Google Scholar
[528] S., Ryu and T., Takayanagi, “Topological insulators and superconductors from string theory,” Phys. Rev. D 82, 086014 (2010) [arXiv:1007.4234 [hep-th]].Google Scholar
[529] A., Karch, J., Maciejko and T., Takayanagi, “Holographic fractional topological insulators in 2 + 1 and 1 + 1 dimensions,” Phys. Rev. D 82, 126003 (2010) [arXiv:1009.2991 [hep-th]].Google Scholar
[530] S., Franco, A., Hanany, D., Martelli, J., Sparks, D., Vegh and B., Wecht, “Gauge theories from toric geometry and brane tilings,” JHEP 0601, 128 (2006) [arXiv:0505211 [hep-th]].Google Scholar
[531] H., Li and F. D. M., Haldane, “Entanglement spectrum as a generalization of entanglement entropy: identification of topological order in non-Abelian fractional quantum Hall effect states,” Phys. Rev. Lett. 101, 010504 (2008) [arXiv:0805.0332 [cond-mat.mes-hall]].Google Scholar
[532] D. M., Greenberger,M. A., Horne and A., Zeilinger, “Going beyond Bell's theorem,” in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, Kluwer, 1989.
[533] D., Bouwmeester, J. W., Pan, M., Daniell, H., Weinfurter and A., Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345 (1999) [arXiv:9810035 [quant-ph]].Google Scholar
[534] M., Srednicki, “Entropy and area,” Phys. Rev. Lett. 71, 666 (1993) [arXiv:9303048 [hep-th]].Google Scholar
[535] C., Holzhey, F., Larsen and F., Wilczek, “Geometric and renormalized entropy in conformal field theory,” Nucl. Phys. B 424, 443 (1994) [arXiv:9403108 [hep-th]].Google Scholar
[536] H. W. J., Bloete, J. L., Cardy and M. P., Nightingale, “Conformal invariance, the central charge, and universal finite size amplitudes at criticality,” Phys. Rev. Lett. 56, 742 (1986).Google Scholar
[537] A., Kitaev and J., Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96, 110404 (2006) [arXiv:0510092 [hep-th]].Google Scholar
[538] M., Levin and X.-G., Wen, “Detecting topological order in a ground state wave function,” Phys. Rev. Lett. 96, 110405 (2006) [arXiv:0510613 [cond-mat.str-el]].Google Scholar
[539] L., Bombelli, R. K., Koul, J., Lee and R. D., Sorkin, “A quantum source of entropy for black holes,” Phys. Rev. D 34, 373 (1986).Google Scholar
[540] S., Ryu and T., Takayanagi, “Aspects of holographic entanglement entropy,” JHEP 0608, 045 (2006) [arXiv:0605073 [hep-th]].Google Scholar
[541] H., Liu and M., Mezei, “A refinement of entanglement entropy and the number of degrees of freedom,” JHEP 1304, 162 (2013) [arXiv:1202.2070 [hep-th]].Google Scholar
[542] R. C., Myers and A., Singh, “Comments on holographic entanglement entropy and RG flows,” JHEP 1204, 122 (2012) [arXiv:1202.2068 [hep-th]].Google Scholar
[543] T., Grover, “Entanglement monotonicity and the stability of gauge theories in three spacetime dimensions,” Phys. Rev. Lett. 112, 151601 (2014) [arXiv:1211.1392 [hep-th]].Google Scholar
[544] M., M. Wolf, “Violation of the entropic area law for fermions,” Phys. Rev. Lett. 96, 010404 (2006) [arXiv:0503219 [quant-ph]].Google Scholar
[545] A., Chandran, V., Khemani and S. L., Sondhi, “How universal is the entanglement spectrum?Phys. Rev. Lett. 113, 060501 (2014) [arXiv:1311.2946 [cond-mat. str-el]].Google Scholar
[546] S., Ryu and T., Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96, 181602 (2006) [arXiv:0603001 [hep-th]].Google Scholar
[547] T., Nishioka, S., Ryu and T., Takayanagi, “Holographic entanglement entropy: an overview,” J. Phys. A 42, 504008 (2009) [arXiv:0905.0932 [hep-th]].Google Scholar
[548] T., Takayanagi, “Entanglement entropy from a holographic viewpoint,” Class. Quant. Grav. 29, 153001 (2012) [arXiv:1204.2450 [gr-qc]].Google Scholar
[549] T., Hartman, “Entanglement entropy at large central charge” [arXiv:1303.6955 [hepth]].
[550] T., Faulkner, “The entanglement Rényi entropies of disjoint intervals in AdS/CFT” [arXiv:1303.7221 [hep-th]].
[551] A., Lewkowycz and J., Maldacena, “Generalized gravitational entropy,” JHEP 1308, 090 (2013) [arXiv:1304.4926 [hep-th]].Google Scholar
[552] J. de, Boer, M., Kulaxizi and A., Parnachev, “Holographic entanglement entropy in Lovelock gravities,” JHEP 1107, 109 (2011) [arXiv:1101.5781 [hep-th]].Google Scholar
[553] L. Y., Hung, R. C., Myers and M., Smolkin, “On holographic entanglement entropy and higher curvature gravity,” JHEP 1104, 025 (2011) [arXiv:1101.5813 [hep-th]].Google Scholar
[554] X., Dong, “Holographic entanglement entropy for general higher derivative gravity,” JHEP 1401, 044 (2014) [arXiv:1310.5713 [hep-th]].Google Scholar
[555] J., Camps, “Generalized entropy and higher derivative gravity,” JHEP 1403, 070 (2014) [arXiv:1310.6659 [hep-th]].Google Scholar
[556] J. D., Brown and M., Henneaux, “Central charges in the canonical realization of asymptotic symmetries: an example from three dimensional gravity,” Comm. Math. Phys. 104, 207 (1986).Google Scholar
[557] A., Strominger, “Black hole entropy from near horizon microstates,” JHEP 9802, 009 (1998) [arXiv:9712251 [hep-th]].Google Scholar
[558] R. C., Myers and A., Sinha, “Holographic c-theorems in arbitrary dimensions,” JHEP 1101, 125 (2011) [arXiv:1011.5819 [hep-th]].Google Scholar
[559] D. L., Jafferis, I. R., Klebanov, S. S., Pufu and B. R., Safdi, “Towards the Ftheorem: N = 2 field theories on the three-sphere,” JHEP 1106, 102 (2011) [arXiv:1103.1181 [hep-th]].Google Scholar
[560] H., Casini, M., Huerta and R. C., Myers, “Towards a derivation of holographic entanglement entropy,” JHEP 1105, 036 (2011) [arXiv:1102.0440 [hep-th]].Google Scholar
[561] N., Ogawa, T., Takayanagi and T., Ugajin, “Holographic Fermi surfaces and entanglement entropy,” JHEP 1201, 125 (2012) [arXiv:1111.1023 [hep-th]].Google Scholar
[562] B., Swingle, “Entanglement entropy and the Fermi surface,” Phys. Rev. Lett. 105, 050502 (2010) [arXiv:0908.1724 [cond-mat.str-el]].Google Scholar
[563] J., Bhattacharya, M., Nozaki, T., Takayanagi and T., Ugajin, “Thermodynamical property of entanglement entropy for excited states,” Phys. Rev. Lett. 110, 091602 (2013) [arXiv:1212.1164 [hep-th]].Google Scholar
[564] F., Kruger and J., Zaanen, “Fermionic quantum criticality and the fractal nodal surface,” Phys. Rev. B 78, 035104 (2008) [arXiv:0804.2161 [cond-mat.str-el]].Google Scholar
[565] D. M., Ceperley, “Fermion nodes,” J. Statist. Phys. 63, 1237 (1991).Google Scholar
[566] M., Van Raamsdonk, “Comments on quantum gravity and entanglement” [arXiv: 0907.2939 [hep-th]].
[567] M., Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42, 2323 (2010) [republished Int. J. Mod. Phys. D 19, 2429 (2010)] [arXiv:1005.3035 [hep-th]].Google Scholar
[568] N., Lashkari, M. B., McDermott and M. Van, Raamsdonk, “Gravitational dynamics from entanglement ‘thermodynamics’,” JHEP 1404, 195 (2014) [arXiv:1308.3716 [hep-th]].Google Scholar
[569] T., Faulkner, M., Guica, T., Hartman, R. C., Myers and M. Van, Raamsdonk, “Gravitation from entanglement in holographic CFTs,” JHEP 1403, 051 (2014) [arXiv:1312.7856 [hep-th]].Google Scholar
[570] D. D., Blanco, H., Casini, L. Y., Hung and R. C., Myers, “Relative entropy and holography,” JHEP 1308, 060 (2013) [arXiv:1305.3182 [hep-th]].Google Scholar
[571] B., Czech, J. L., Karczmarek, F., Nogueira and M., Van Raamsdonk, “The gravity dual of a density matrix,” Class. Quant. Grav. 29, 155009 (2012) [arXiv:1204.1330 [hep-th]].Google Scholar
[572] B., Czech, J. L., Karczmarek, F., Nogueira and M., Van Raamsdonk, “Rindler quantum gravity,” Class. Quant. Grav. 29, 235025 (2012) [arXiv:1206.1323 [hep-th]].Google Scholar

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  • References
  • Jan Zaanen, Universiteit Leiden, Yan Liu, Universidad Autónoma de Madrid, Ya-Wen Sun, Universidad Autónoma de Madrid, Koenraad Schalm, Universiteit Leiden
  • Book: Holographic Duality in Condensed Matter Physics
  • Online publication: 05 November 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139942492.016
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  • References
  • Jan Zaanen, Universiteit Leiden, Yan Liu, Universidad Autónoma de Madrid, Ya-Wen Sun, Universidad Autónoma de Madrid, Koenraad Schalm, Universiteit Leiden
  • Book: Holographic Duality in Condensed Matter Physics
  • Online publication: 05 November 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139942492.016
Available formats
×

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  • References
  • Jan Zaanen, Universiteit Leiden, Yan Liu, Universidad Autónoma de Madrid, Ya-Wen Sun, Universidad Autónoma de Madrid, Koenraad Schalm, Universiteit Leiden
  • Book: Holographic Duality in Condensed Matter Physics
  • Online publication: 05 November 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139942492.016
Available formats
×