Book contents
- Frontmatter
- Contents
- Preface
- List of contributors
- List of figures
- List of tables
- Part One Einstein's Triumph
- Part Two New Window on the Universe: Gravitational Waves
- Part Three Gravity is Geometry, after all
- Part Four Beyond Einstein
- 10 Quantum Fields in Curved Spacetime
- 11 From General Relativity to Quantum Gravity
- 12 Quantum Gravity via Supersymmetry and Holography
- Index
- References
12 - Quantum Gravity via Supersymmetry and Holography
from Part Four - Beyond Einstein
Published online by Cambridge University Press: 05 June 2015
Book contents
- Frontmatter
- Contents
- Preface
- List of contributors
- List of figures
- List of tables
- Part One Einstein's Triumph
- Part Two New Window on the Universe: Gravitational Waves
- Part Three Gravity is Geometry, after all
- Part Four Beyond Einstein
- 10 Quantum Fields in Curved Spacetime
- 11 From General Relativity to Quantum Gravity
- 12 Quantum Gravity via Supersymmetry and Holography
- Index
- References
Summary
This chapter offers a survey of ideas and results in the approach to quantum gravity based on supersymmetry, strings, and holography.
Extra spatial dimensions appear naturally in this approach, so to set the stage we begin in Section 12.1 with a discussion of general relativity in more than four spacetime dimensions. In higher dimensions, one encounters a richness of structure with no parallel in 4D. Even in vacuum gravity, this includes black hole solutions with non-spherical horizon topologies, black hole non-uniqueness, and regular multi-horizon black holes. We give an overview of such solutions and their properties, both in the context of Kaluza–Klein theory and for asymptotically flat boundary conditions.
A very interesting extension of general relativity is to include matter in such a way that the action becomes invariant under supersymmetry transformations. Supersymmetry is a remarkable symmetry that relates bosons and fermions. It is the only possible extension of the Poincaré group for a unitary theory with non-trivial scattering processes. Supersymmetry is considered a natural extension of the standard model of particle physics; the study of how supersymmetry is broken at low energies, and its possible experimental consequences, is an important active research area in particle physics. Furthermore, independently of its potential phenomenology, supersymmetry offers strong calculational control and that makes it a tremendously powerful tool for analyzing fundamental properties of quantum field theories.
When supersymmetry and general relativity are combined, the result is supergravity. The metric field is accompanied by a spin-3/2 spinor field and this gives a beautiful and enticing playground for advancing our understanding of quantum gravity. Supergravity theories exist in spacetime dimensions D ≤ 11 and they provide a natural setting for studies of charged black holes. Certain extremal limits of charged black holes in super-gravity are invariant under supersymmetry; such ‘supersymmetric black holes’ are key for understanding the statistical mechanical nature of black hole thermodynamics, specifically the microstates responsible for the Hawking–Bekenstein entropy. An example of a super- symmetric black hole is the extremal Reissner–Nordström solution.
- Type
- Chapter
- Information
- General Relativity and GravitationA Centennial Perspective, pp. 612 - 666Publisher: Cambridge University PressPrint publication year: 2015
References
[1] , “Schwarzschild field in n dimensions and the dimensionality of space problem,”Nuovo Cim. 27 (1963) 636.Google Scholar
[2] and , “The Black hole in three-dimensional space-time,”Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099].Google Scholar
[3] , “On the Problem of Unity in Physics,”Sitzungsber. Preuss. Akad. Wiss. (1921) 966.Google Scholar
[4] , “Quantum Theory and Five-Dimensional Theory of Relativity (in German and English),”Z. Phys. 37 (1926) 895 [Surveys High Energy Phys. 5 (1986) 241].Google Scholar
[5] and , “Black strings and p-branes are unstable,”Phys. Rev. Lett. 70(1993) 2837 [hep-th/9301052].Google Scholar
[6] and , “General black holes in Kaluza-Klein theory,” in Blackholes in higher dimensions( ed.), Cambridge: Cambridge University Press (2012); arXiv:1107.5563 [gr-qc].Google Scholar
[7] and , The large scale structure of space-time, Cambridge: Cambridge University Press, (1973).Google Scholar
[8] and , “Fate of the black string instability,”Phys.Rev. Lett. 87 (2001) 131301 [hep-th/0105111].Google Scholar
[10] and , “Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings,”Phys. Rev. Lett. 96(2006) 181601 [hep-th/0602017].Google Scholar
[11] , “Static axisymmetric vacuum solutions and nonuniform black strings,”Class. Quant. Grav. 20 (2003) 1137 [hep-th/0209051].Google Scholar
[12] and , “Properties of Kaluza-Klein black holes,”Prog. Theor. Phys. 111(2004) 475 [hep-th/0310104].Google Scholar
[13] and , “New nonuniform black string solutions,”JHEP 0606, 016 (2006) [hep-th/0603119].Google Scholar
[14] and , “Gravitational Energy in Spaces With Compactified Dimensions,”Nucl. Phys. B 311 (1989) 739.Google Scholar
[15] and , “States of Negative Total Energy in Kaluza-Klein Theory,”Phys. Lett. B 228 (1989) 359.Google Scholar
[18] , “A positive energy theorem for spaces with asymptotic SUSY compactification,”Commun. Math. Phys. 244 (2004) 335.Google Scholar
[19] and , “When black holes meet Kaluza-Klein bubbles,”Phys. Rev. D 67 (2003) 044015 [hep-th/0210303].Google Scholar
[20] and , “Sequences of bubbles and holes: New phases of Kaluza-Klein black holes,”JHEP0501 (2005) 003 [hep-th/0407050].Google Scholar
[21] and , “Black Holes in Higher Dimensional Space-Times,”Annals of Physics 172 (1986)304.Google Scholar
[22] and , “A Rotating black ring solution in five-dimensions,”Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260].Google Scholar
[24] , “A Charged rotating black ring,”Phys. Rev. D 68 (2003) 124016 [hep-th/0305247].Google Scholar
[25] and A. Virmani, “Dynamics and stability of black rings,”JHEP 0612(2006) 074 [hep-th/0608076].Google Scholar
[26] and , “Phases of five-dimensional black holes,”JHEP 0705(2007) 056 [hep-th/0702111].Google Scholar
[27] and , “Black ring with two angular momenta,” hep-th/0612005.
[28] and , “Integration of the Einstein Equations by the Inverse Scattering Problem Technique and the Calculation of the Exact Soliton Solutions,”Sov. Phys. JETP 48 (1978) 985 [Zh. Eksp. Teor. Fiz. 75 (1978) 1953].Google Scholar
[29] and , “Stationary Gravitational Solitons with Axial Symmetry,”Sov. Phys. JETP 50 (1979) 1 [Zh. Eksp. Teor. Fiz. 77 (1979) 3].Google Scholar
[33] . Chruściel and , “On smoothness of Black Saturns,”JHEP 1011 (2010) 048 [arXiv:1007.3668 [hep-th]].Google Scholar
[34] and , “Black di-ring and infinite nonuniqueness,”Phys. Rev. D 75, 064018 (2007) [Erratum ibid.D 78, 069903 (2008] [hep-th/0701043].Google Scholar
[35] and , “The Black Di-Ring: An Inverse Scattering Construction,”Class. Quant. Grav. 26, 125018 (2009) [arXiv:0706.1231 [hep-th]].Google Scholar
[36] , “Orthogonal black di-ring solution,”Prog. Theor. Phys. 119 (2008) 757 [arXiv:0712.0902 [hep-th]].Google Scholar
[37] , “Higher dimensional black holes and supersymmetry,”Phys. Rev. D 68 (2003) 024024 [Erratum ibid. D 70 (2004) 089902] [hep-th/0211290].Google Scholar
[38] and , “A Higher dimensional stationary rotating black hole must be axisymmetric,”Commun. Math. Phys. 271 (2007) 699 [gr-qc/0605106].Google Scholar
[39] and , “Symmetries of Higher Dimensional Black Holes,”Class. Quant. Grav. 25 (2008) 195015 [arXiv:0805.1451 [gr-qc]].Google Scholar
[40] and , “New Horizons for Black Holes and Branes,”JHEP 1004 (2010) 046 [arXiv:0912.2352 [hep-th]].Google Scholar
[41] and . Myers, “Instability of ultra-spinning black holes,”JHEP 0309 (2003) 025 [hep-th/0308056].Google Scholar
[42] and . Reall, “Black Holes in Higher Dimensions,”Living. 11 (2008) 6 [arXiv:0801.3471 [hep-th]].Google Scholar
[43] and , “The Phase Structure of Higher-Dimensional Black Rings and Black Holes,”JHEP 0710, 110 (2007) [arXiv:0708.2181 [hep-th]].Google Scholar
[44] and , “Essentials of Blackfold Dynamics,”JHEP 1003 (2010) 063 [arXiv:0910.1601 [hep-th]].Google Scholar
[45] and , “World-Volume Effective Theory for Higher-Dimensional Black Holes,”Phys.Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427 [hep-th]].Google Scholar
[46] and , “Derivation of the blackfold effective theory,”JHEP 1203 (2012) 038 [Erratum ibid. 1206 (2012) 155] [arXiv:1201.3506 [hep-th]].Google Scholar
[47] and , “Black rings in six dimensions,”Phys.Lett. B 718, 1073 (2013) [arXiv:1205.5437 [hep-th]].Google Scholar
[49] and , “All Possible Generators of Supersymmetries of the S Matrix,”Nucl.Phys. B 88 (1975) 257.Google Scholar
[50] and , Supersymmetry and supergravity, Princeton, NJ: Princeton University Press (1992).Google Scholar
[54] and Nieuwenhuizen, “Consistent Supergravity with Complex Spin 3/2 Gauge Fields,”Phys.Rev.|Lett. 37 (1976) 1669.Google Scholar
[55] , “Supergravities in Five Dimensions,” in Superspace and supergravity. Proceedings, Nuffield Workshop, Cambridge, UK, June 16-July 12, 1980,” Eds. and , Cambridge: Cambridge University Press (1981).Google Scholar
[57] and , “Cubic Interaction in Extended Theories of Massless higher spin fields,”Nucl.Phys.|B 291, 141 (1987).Google Scholar
[58] , “Higher spin gauge theories: star product and AdS space,” in . (ed.): The many faces of the superworld, pp. 533–610 [hep-th/9910096].
[59] and , “AdS dual of the critical O(N) vector model,”Phys.Lett. B 550, 213 (2002) [hep-th/0210114].Google Scholar
[60] and , “An AdS3 Dual for Minimal Model CFTs,”Phys.Rev. D 83, 066007 (2011) [arXiv:1011.2986 [hep-th]].Google Scholar
[62] and , “Gauged N = 8 Supergravity in Five-Dimensions,”Phys.Lett. B 154 (1985) 268.Google Scholar
[63] , “Stability of Classical Solutions,”Sov. J. Nucl. Phys. 24, 449 (1976) [Yad.|Fiz. 24, 861 (1976)].Google Scholar
[64] and , “An Exact Classical Solution for the't Hooft Monopole and the Julia-Zee Dyon,”Phys.Rev.|Lett. 35 (1975) 760.Google Scholar
[65] , “A Simple Proof of the Positive Energy Theorem,”Commun.Math. Phys. 80 (1981) 381.Google Scholar
[66] and , “A Bogomol'nyi Bound for General Relativity and Solitons in N = 2 Supergravity,”Phys.Lett. B 109 (1982) 190.Google Scholar
[67] P.K.|Townsend and , “Supersym-metric selfgravitating solitons,”Nucl.Phys. B 416 (1994) 850 [hep-th/9310118].Google Scholar
[68] and , “General rotating five-dimensional black holes of toroidally compactified heterotic string,”Nucl.Phys. B 476, 118 (1996) [hep-th/9603100].Google Scholar
[69] and , “D-branes and spinning black holes,”Phys. Lett.B 391 (1997) 93 [hep-th/9602065].Google Scholar
[70] and , “A Supersymmetric black ring,”Phys.Rev. Lett. 93 (2004) 211302 [hep-th/0407065].Google Scholar
[71] and , “One ring to rule them all… and in the darkness bind them?,”Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106].Google Scholar
[72] and , “Supersymmetric black rings and three-charge supertubes,”Phys.Rev. D 71 (2005) 024033 [hep-th/0408120].Google Scholar
[73] and , “General concentric black rings,”Phys.Rev. D 71 (2005) 045002 [hep-th/0408122].Google Scholar
[75] and , “Scattering Amplitudes and the Positive Grassmannian,” arXiv:1212.5605 [hep-th].Google Scholar
[76] and , “A Relation Between Tree Amplitudes of Closed and Open Strings,”Nucl.Phys. B 269, 1 (1986).Google Scholar
[77] and , “Multileg one loop gravity amplitudes from gauge theory,”Nucl.Phys. B 546, 423 (1999) [hep-th/9811140].Google Scholar
[78] and , “Perturbative gravity from QCD amplitudes,”Phys.Lett. B 457, 23 (1999) [hep-th/9904026].Google Scholar
[79] and , “On perturbative gravity and gauge theory,”Nucl. Phys. Proc.Suppl. 88, 194 (2000) [hep-th/0002078].Google Scholar
[80] , “Two vierbein formalism for string inspired axionic gravity,”Phys.Rev. D 47, 5453 (1993) [hep-th/9302036].Google Scholar
[81] , “Perturbative quantum gravity and its relation to gauge theory,”Living Rev. Rel. 5, 5 (2002) [gr-qc/0206071].Google Scholar
[82] and , “New Relations for Gauge-Theory Amplitudes,”Phys.Rev. D 78, 085011 (2008) [arXiv:0805.3993 [hep-ph]].Google Scholar
[83] and , “One loop divergencies in the theory of gravitation,”Ann.Inst. Henri Poincare Phys.Theor. A 20, 69 (1974).Google Scholar
[86] and , “One Loop Divergences of Quantized Einstein-Maxwell Fields,”Phys.Rev. D 10, 401 (1974).Google Scholar
[87] and , “One Loop Renormalizability of Pure Supergravity and of Maxwell-Einstein Theory in Extended Supergravity,”Phys.Rev.|Lett. 37, 1662(1976).Google Scholar
[89] , “On the Two Loop Divergences of Supersymmetric Gravitation,”Phys.Lett. B 67, 417 (1977).Google Scholar
[90] and , “Renormalizability Properties of Supergravity,”Phys.Rev. Lett. 38, 527 (1977).Google Scholar
[91] and , “The Ultraviolet Properties of N = 4 Supergravity at Four Loops,” arXiv:1309.2498 [hep-th].Google Scholar
[92] and , “Is N = 8 supergravity ultraviolet finite?,”Phys.Lett. B 644, 265 (2007) [hep-th/0611086].Google Scholar
[93] and , “Three-Loop Superfiniteness of N = 8 Supergravity,”Phys.Rev. Lett. 98, 161303 (2007) [hep-th/0702112].Google Scholar
[94] and , “Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N = 8 Supergravity,”Phys.Rev.D 78, 105019 (2008) [arXiv:0808.4112 [hep-th]].Google Scholar
[95] and , “The Ultraviolet Behavior of N = 8 Supergravity at Four Loops,”Phys.Rev.Lett. 103, 081301 (2009) [arXiv:0905.2326 [hep-th]].Google Scholar
[96] and , “The Complete Four-Loop Four-Point Amplitude in N = 4 Super-Yang-Mills Theory,”Phys.Rev. D 82, 125040 (2010) [arXiv:1008.3327 [hep-th]].Google Scholar
[97] and , “A simple approach to counterterms in N = 8 supergravity,”JHEP 1011, 016 (2010) [arXiv:1003.5018 [hep-th]].Google Scholar
[99] and , “Stringy KLT relations, global symmetries, and E7(7) violation,”JHEP 1010, 108 (2010) [arXiv:1007.4813 [hep-th]].Google Scholar
[100] and , “E7(7) constraints on counterterms in N = 8 supergravity,”Phys.Lett. B 694, 265 (2010) [arXiv:1009.1643 [hep-th]].Google Scholar
[101] and , “Modular properties of two-loop maximal supergravity and connections with string theory,”JHEP 0807, 126 (2008) [arXiv:0807.0389 [hep-th]].Google Scholar
[102] and , “The vanishing volume of D = 4 superspace,”Class. Quant. Grav. 28, 215005 (2011) [arXiv:1105.6087 [hep-th]].Google Scholar
[103] , A first course in string theory, Cambridge: Cambridge University Press (2009).Google Scholar
[104] , String theory. Vol. 1. An introduction to the bosonic string, Cambridge: Cambridge University Press (1998); String theory. Vol. 2. Superstring theory and beyond, Cambridge: Cambridge University Press (1998).Google Scholar
[105] and String theory and M-theory: a modern introduction, Cambridge: Cambridge University Press (2007).Google Scholar
[106] , and , “Supersymmetry, supergravity, and the dual spinor model,”Nucl. Phys. B122 (1977) 253.Google Scholar
[108] , “Noncommutative Geometry and String Field Theory,”Nucl. Phys. B268 (1986) 253.Google Scholar
[109] , “Universality of the tachyon potential,”JHEP 9912 (1999) 027 [hep-th/9911116].Google Scholar
[110] and , “Level truncation and the tachyon in open bosonic string field theory,”Nucl. Phys. B 583 (2000) 105. [hep-th/0002237].Google Scholar
[114] and , “Target space duality in string theory,”Phys. Rept. 244 (1994) 77 [hep-th/9401139].Google Scholar
[115] and “Chiral Rings in N = 2 Superconformal Theories,”Nucl. Phys. B 324 (1989) 427.Google Scholar
[117] and , “A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory,”Nucl.|Phys. B 359 (1991) 21.Google Scholar
[118] and , “Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory,”Nucl. Phys. B 416 (1994) 414 [hep-th/9309097].Google Scholar
[121] and , “Anomaly Cancellation in Supersymmetric D = 10 Gauge Theory and Superstring Theory,”Phys. Lett. B 149 (1984) 117.Google Scholar
[122] , “Dirichlet Branes and Ramond-Ramond charges,”Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017].Google Scholar
[123] and , “De Sitter vacua in string theory,”Phys.|Rev. D 68 (2003) 046005 [hep-th/0301240].Google Scholar
[124] , “String theory dynamics in various dimensions,”Nucl. Phys. B 443 (1995) 85 [hep-th/9503124].Google Scholar
[125] and , “M theory as a matrix model: a conjecture,”Phys. Rev. D 55 (1997) 5112 [hep-th/9610043].Google Scholar
[126] , “Some speculations about black hole entropy in string theory,” in (ed.): The black hole, pp. 118–131 [hep-th/9309145].
[127] and , “A correspondence principle for black holes and strings,”Phys. Rev. D 55 (1997) 6189 [hep-th/9612146].Google Scholar
[128] and , “Microscopic origin of the Bekenstein-Hawking entropy,”Phys. Lett. B 379 (1996) 99 [hep-th/9601029].Google Scholar
[129] and “D-brane approach to black hole quantum mechanics,”Nucl. Phys. B 472 (1996) 591 [hep-th/9602043].Google Scholar
[130] and , “Counting states of near extremal black holes,”Phys. Rev. Lett. 77 (1996) 2368 [hep-th/9602051].Google Scholar
[131] and , “Statistical entropy of four-dimensional extremal black holes,”Phys. Rev. Lett. 77 (1996) 428 [hep-th/9603060].Google Scholar
[132] and “Entropy of 4-D extremal black holes,”Phys. Lett. B 378 (1996) 78 [hep-th/9603061].Google Scholar
[133] and “Statistical entropy of nonextremal four-dimensional black holes and U duality,”Phys. Rev. Lett. 77 (1996) 430 [hep-th/9603195].Google Scholar
[134] and , “Black hole grey body factors and d-brane spectroscopy,”Phys. Rev. D 55 (1997) 861 [hep-th/9609026].Google Scholar
[135] and “Comparing decay rates for black holes and D-branes,”Nucl. Phys. B 478 (1996) 561 [hep-th/9606185].Google Scholar
[136] and , “Microscopic entropy of the black ring,”Phys.|Rev. Lett. 94, 191601 (2005) [hep-th/0411187].Google Scholar
[137] and , “Microscopic description of black rings in AdS/CFT,”JHEP 0412, 070 (2004) [hep-th/0408186].Google Scholar
[138] and , “Microstates of the D1-D5-KK system,”Phys. Rev. D 72, 025007 (2005) [hep-th/0503053].Google Scholar
[139] , “Dimensional reduction in quantum gravity,” gr-qc/9310026.
[141] and , “Quantum Field Theory in anti-De Sitter space-time,”Phys.|Rev. D 18 (1978) 3565.Google Scholar
[142] and “Thermodynamics of Black Holes in anti-De Sitter space,”Commun.|Math. Phys. 87 (1983) 577.Google Scholar
[143] , “Unitarity and Holography in Gravitational Physics,”Phys.Rev.D 79 (2009) 044010 [arXiv:0808.2842 [gr-qc]].Google Scholar
[144] “The large N limit of superconformal field theories and supergravity,”Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200].Google Scholar
[145] and “Entropy and temperature of black 3-branes,”Phys. Rev. D 54 (1996) 3915 [hep-th/9602135].Google Scholar
[146] and “Gauge theory correlators from noncritical string theory,”Phys. Lett. B 428 (1998) 105 [hep-th/9802109].Google Scholar
[147] , “Anti-de Sitter space and holography,”Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150].Google Scholar
[148] and “An Exact prediction of N = 4 SUSYM theory for string theory,”J. Math. Phys. 42 (2001) 2896 [hep-th/0010274].Google Scholar
[149] and “Renormalization group flows from holography supersymmetry and a c theorem,”Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017].Google Scholar
[150] and “Strings in flat space and pp waves from N = 4 superYang-Mills,”JHEP 0204 (2002) 013 [hep-th/0202021].Google Scholar
[151] and “Bubbling AdS space and 1/2 BPS geometries,”JHEP 0410 (2004) 025 [hep-th/0409174].Google Scholar
[152] and , “AdS(3) black holes and a stringy exclusion principle,”JHEP 9812 (1998) 005 [hep-th/9804085].Google Scholar
[153] and , “Invasion of the giant gravitons from anti-de Sitter space,”JHEP 0006 (2000) 008 [hep-th/0003075].Google Scholar
[155] and , “N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,”JHEP 0810 (2008) 091 [arXiv:0806.1218 [hep-th]].Google Scholar
[156] and , “Superconformal field theory on three-branes at a Calabi-Yau singularity,”Nucl. Phys. B 536 (1998) 199 [hep-th/9807080].Google Scholar
[157] and , “The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere,”Nucl.|Phys. B 866 (2013) 72 [arXiv:1111.6930 [hep-th]].Google Scholar
[158] and , “The Holography of F-maximization,” arXiv:1302. 7310 [hep-th].
[159] “Breakdown of Predictability in Gravitational Collapse,”Phys.Rev.D 14(1976) 2460.Google Scholar
[160] “The Information paradox: A Pedagogical introduction,”Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038 [hep-th]].Google Scholar
[161] “Fuzzballs and the information paradox: A Summary and conjectures,” arXiv:0810.4525 [hep-th].
[162] and , “Black Holes: Complementarity or Firewalls?,”JHEP 1302 (2013) 062 [arXiv:1207.3123 [hep-th]]; S.L.|Braunstein, “Black hole entropy as entropy of entanglement, or it's curtains for the equivalence principle,” [arXiv:0907.1190v1 [quant-ph]] published as and , “Better late than never: information retrieval from black holes,” Phys.|Rev. Lett. 110, 101301 (2013) for a similar prediction from different assumptions.Google Scholar
[163] and , “A Stress tensor for Anti-de Sitter gravity,”Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121].Google Scholar
[164] and “The AdS/CFT correspondence and a new positive energy conjecture for general relativity,”Phys. Rev. D 59 (1998) 026005 [hep-th/9808079].Google Scholar
[165] and , “Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence,”Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230].Google Scholar
[166] and “Viscosity in strongly interacting quantum field theories from black hole physics,”Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231].Google Scholar
[167] and , “Holographic turbulence,”Phys. Rev. Lett. 112 (2014) 15, 151602 [arXiv:1307.7267 [hep-th]].Google Scholar
[168] “Breaking an Abelian gauge symmetry near a black hole horizon,”Phys.|Rev. D 78 (2008) 065034 [arXiv:0801.2977 [hep-th]].Google Scholar
[169] and , “Building a Holographic Superconductor,”Phys. Rev. Lett. 101 (2008)031601 [arXiv:0803.3295 [hep-th]].Google Scholar
[170] and , “Optical Conductivity with Holographic Lattices,”JHEP 1207 (2012) 168 [arXiv:1204.0519 [hep-th]].Google Scholar
[171] and “General Relativity and the Cuprates,”JHEP 1306 (2013) 087 [arXiv:1302.6586 [hep-th]].Google Scholar
[172] and , “Holographic derivation of entanglement entropy from AdS/CFT,”Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001].Google Scholar
[173] and , “Holographic Entanglement Entropy: An overview,”J. Phys. A 42 (2009) 504008 [arXiv: 0905.0932 [hep-th]].Google Scholar
[174] and , “Generalized gravitational entropy,”JHEP 1308 (2013) 090 [arXiv:1304.4926 [hep-th]].Google Scholar
[175] , “Building up space-time with quantum entanglement,”Gen. Rel. Grav. 42 (2010) 2323 [Int. J. Mod. Phys. D 19 (2010) 2429][arXiv:1005.3035[hep-th]].Google Scholar