Skip to main content Accessibility help
×
Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-16T20:38:36.582Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 September 2015

Marcos Mariño
Affiliation:
Université de Genève
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Instantons and Large N
An Introduction to Non-Perturbative Methods in Quantum Field Theory
, pp. 356 - 364
Publisher: Cambridge University Press
Print publication year: 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Adams, D. 1996. Perturbative expansion in gauge theories on compact manifolds. hep-th/9602078.
[2] Affleck, I. 1980. Testing the instanton method. Phys. Lett., B 92, 149–152.CrossRefGoogle Scholar
[3] Affleck, I. 1981. Quantum statistical metastability. Phys. Rev. Lett., 46, 388–391.CrossRefGoogle Scholar
[4] Affleck, I. 1981. Mesons in the large N collective field method. Nucl. Phys., B 185, 346–364.CrossRefGoogle Scholar
[5] Aguado, M. and Asorey, M. 2011. Theta-vacuum and large N limit in CPN−1 sigma models. Nucl. Phys., B 844, 243–265.CrossRefGoogle Scholar
[6] Aharony, O., Gubser, S. S., Maldacena, J. M., Ooguri, H. and Oz, Y. 1990. Large N field theories, string theory and gravity. Phys. Rep., 323, 183–386.Google Scholar
[7] Akemann, G., Baik, J. and Di Francesco, P. (eds.) 2011. The Oxford Handbook ofRandom Matrix Theory. Oxford University Press.Google Scholar
[8] Akhiezer, N. I. 1990. Elements of the Theory of Elliptic Functions. American Mathematical Society.CrossRefGoogle Scholar
[9] Altland, A. and Simons, B. 2006. Condensed Matter Field Theory. Cambridge University Press.CrossRefGoogle Scholar
[10] Álvarez, G. 1988. Coupling-constant behavior of the resonances of the cubic anharmonic oscillator. Phys. Rev., A 37, 4079–4083.CrossRefGoogle ScholarPubMed
[11] Álvarez, G. 2004. Langer–Cherry derivation of the multi-instanton expansion for the symmetric double well. J. Math. Phys., 45, 3095–3108.CrossRefGoogle Scholar
[12] Álvarez-Gaumé, L. and Vázquez-Mozo, M. A. 2012. An Invitation to Quantum Field Theory. Springer-Verlag.CrossRefGoogle Scholar
[13] Ambjorn, J., Chekhov, L., Kristjansen, C. F. and Makeenko, Y. 1993 Matrix model calculations beyond the spherical limit. Nucl. Phys., B 404, 127–172.CrossRefGoogle Scholar
[14] Aniceto, I., Schiappa, R. and Vonk, M. 2012. The resurgence of instantons in string theory. Commun. Num. Theor. Phys., 6, 339–496.CrossRefGoogle Scholar
[15] Appelquist, T. and Chodos, A. 1983. The quantum dynamics of Kaluza–Klein theories. Phys. Rev., D 28, 772–784.Google Scholar
[16] Atiyah, M. F., Hitchin, N. J., Drinfeld, V. G. and Manin, Y. I. 1978. Construction of instantons. Phys. Lett., A 65, 185–187.CrossRefGoogle Scholar
[17] Baacke, J. and Lavrelashvili, G. 2004. One-loop corrections to the metastable vacuum decay. Phys. Rev., D 69, 025009.Google Scholar
[18] Balian, R., Parisi, G. and Voros, A. 1978. Discrepancies from asymptotic series and their relation to complex classical trajectories. Phys. Rev. Lett., 41, 1141–1144.Google Scholar
[19] Balian, R., Parisi, G. and Voros, A. 1979. Quartic oscillator. In: Feynman Path Integrals, Lecture Notes in Physics 106, pp. 337–360, Springer-Verlag.CrossRefGoogle Scholar
[20] Bar-Natan, D. 1995. On the Vassiliev knot invariants. Topology, 34, 423–472.CrossRefGoogle Scholar
[21] Bars, I. and Green, M. B. 1978. Poincare and gauge invariant two-dimensional QCD. Phys. Rev., D 17, 537–545.Google Scholar
[22] Basar, G., Dunne, G. V. and Unsal, M. 2013. Resurgence theory, ghost-instantons, and analytic continuation of path integrals. JHEP, 1310, 041.CrossRefGoogle Scholar
[23] Bauer, C., Bali, G. S. and Pineda, A. 2012. Compelling evidence of renormalons in QCD from high order perturbative expansions. Phys. Rev. Lett., 108, 242002.CrossRefGoogle ScholarPubMed
[24] Belavin, A. A. and Polyakov, A.M. 1977. Quantum fluctuations of pseudoparticles. Nucl. Phys., B 123, 429–444.CrossRefGoogle Scholar
[25] Belavin, A. A., Polyakov, A. M., Schwartz, A. S. and Tyupkin, Y. S. 1975. Pseudoparticle solutions of the Yang–Mills equations. Phys. Lett., B 59, 85–87.CrossRefGoogle Scholar
[26] Bender, C. M. 1978. Perturbation Theory in large order. Adv. Math., 30, 250–267.CrossRefGoogle Scholar
[27] Bender, C. M. and Caswell, W. E. 1978. Asymptotic graph counting techniques in ψ2N field theory. J. Math. Phys., 19, 2579–2586.CrossRefGoogle Scholar
[28] Bender, C. M. and Orszag, S. A. 1999. Advanced Mathematical Methods for Scientists and Engineers. Springer-Verlag.CrossRefGoogle Scholar
[29] Bender, C. M. and Wu, T. T. 1969. Anharmonic oscillator. Phys. Rev., 184, 1231–1260.CrossRefGoogle Scholar
[30] Bender, C.M. and Wu, T. T. 1973. Anharmonic oscillator. 2: a study of perturbation theory in large order. Phys. Rev., D 7, 1620–1636.Google Scholar
[31] Bender, C. M. and Wu, T. T. 1976. Statistical analysis of Feynman diagrams. Phys. Rev. Lett., 37, 117–120.CrossRefGoogle Scholar
[32] Beneke, M. 1999. Renormalons. Phys. Rep., 317, 1–142.CrossRefGoogle Scholar
[33] Berg, B. and Lüscher, M. 1979. Computation of quantum fluctuations around multiinstanton fields from exact Green's functions: the ℂℙN−1 case. Commun. Math. Phys., 69, 57–80.CrossRefGoogle Scholar
[34] Bernard, C. W. 1979. Gauge zero modes, instanton determinants, and QCD calculations. Phys. Rev., D 19, 3013–3019.Google Scholar
[35] Bessis, D., Itzykson, C. and Zuber, J. B. 1980. Quantum field theory techniques in graphical enumeration. Adv. Appl. Math., 1, 109–157.CrossRefGoogle Scholar
[36] Bogomolny, E. B. and Fateev, V. A. 1977. Large order calculations in gauge theories. Phys. Lett., B 71, 93–96.CrossRefGoogle Scholar
[37] Brézin, E. and Wadia, S. (eds.) 1991. The Large N Expansion in Quantum Field Theory and Statistical Physics. World Scientific.Google Scholar
[38] Brézin, E., Le Guillou, J. C. and Zinn-Justin, J. 1977. Perturbation theory at large order. 1. The ψ2N interaction. Phys. Rev., D 15, 1544–1557.Google Scholar
[39] Brézin, E., Le Guillou, J. C. and Zinn-Justin, J. 1977. Perturbation theory at large order. 2. Role of the vacuum instability. Phys. Rev., D 15, 1558–1564.Google Scholar
[40] Brézin, E., Itzykson, C., Parisi, G. and Zuber, J. B. 1978. Planar diagrams. Commun. Math. Phys., 59, 35–51.CrossRefGoogle Scholar
[41] Brower, R. C., Spence, W. L. and Weis, J. H. 1979. Bound states and asymptotic limits for QCD in two-dimensions. Phys. Rev., D 19, 3024–3049.Google Scholar
[42] Caliceti, E., Graffi, S. and Maioli, M. 1980. Perturbation theory of odd anharmonic oscillators. Commun. Math. Phys., 75, 51–66.CrossRefGoogle Scholar
[43] Caliceti, E., Meyer-Hermann, M., Ribeca, P., Surzhykov, A. and Jentschura, U. D. 2007. From useful algorithms for slowly convergent series to physical predictions based on divergent perturbative expansions. Phys. Rep., 446, 1–96.CrossRefGoogle Scholar
[44] Callan, C. G. and Coleman, S. R. 1977. The fate of the false vacuum. 2. First quantum corrections. Phys. Rev., D 16, 1762–1768.Google Scholar
[45] Callan, C. G., Dashen, R. F. and Gross, D. J. 1976. The structure of the gauge theory vacuum.Phys. Lett., B 63, 334–340.CrossRefGoogle Scholar
[46] Chadha, S., Di Vecchia, P., D'Adda, A. and Nicodemi, F. 1977. Zeta function regularization of the quantum fluctuations around the Yang–Mills pseudoparticle. Phys. Lett., B 72, 103–108.CrossRefGoogle Scholar
[47] Christos, G. A. 1984. Chiral symmetry and the U(1) problem. Phys. Rep., 116, 251–336.CrossRefGoogle Scholar
[48] Cicuta, G. M. 1982. Topological expansion for SO(N) and Sp(2n) gauge theories. Lett. Nuovo Cimento, 35 87–92.CrossRefGoogle Scholar
[49] Coleman, S. R. 1977. The fate of the false vacuum. 1. Semiclassical theory. Phys. Rev., D 15, 2929–2936.Google Scholar
[50] Coleman, S. 1985. Aspects of Symmetry. Cambridge University Press.CrossRefGoogle Scholar
[51] Coleman, S. R. and De Luccia, F. 1980. Gravitational effects on and of vacuum decay. Phys. Rev., D 21, 3305–3315.Google Scholar
[52] Coleman, S. R., Glaser, V. and Martin, A. 1978. Action minima among solutions to a class of Euclidean scalar field equations. Commun. Math. Phys., 58, 211–221.CrossRefGoogle Scholar
[53] Collins, J. C. and Soper, D. E. 1978. Large order expansion in perturbation theory. Ann. Phys., 112, 209–234.CrossRefGoogle Scholar
[54] Cooper, F. and Freedman, B. 1983. Aspects of supersymmetric quantum mechanics. Ann. Phys., 146, 262–288.CrossRefGoogle Scholar
[55] Cooper, F., Khare, A. and Sukhatme, U. 1995. Supersymmetry and quantum mechanics. Phys. Rep., 251, 267–385.CrossRefGoogle Scholar
[56] Costin, O. 2009. Asymptotics and Borel Summability. Chapman-Hall.Google Scholar
[57] Cvitanovic, P. 1976. Group theory for Feynman diagrams in non-Abelian gauge theories. Phys. Rev., D 14, 1536–1553.Google Scholar
[58] Cvitanovic, P. 2008. Group Theory: Birdtracks, Lie's and Exceptional groups. Princeton University Press.CrossRefGoogle Scholar
[59] Cvitanovic, P. et al. 2011. Chaos: Classical and Quantum. Gone with the Wind Press. http://chaosbook.org/.Google Scholar
[60] D'Adda, A., Di Vecchia, P. and Luscher, M. 1978. A 1/N expandable series of nonlinear sigma models with instantons. Nucl. Phys., B 146, 63–76.CrossRefGoogle Scholar
[61] D'Adda, A., Di Vecchia, P. and Luscher, M. 1979. Confinement and chiral symmetry breaking in ℂℙn−1 models with quarks. Nucl. Phys., B 152, 125–144.CrossRefGoogle Scholar
[62] Daniel, M. and Viallet, C. M. 1980. The geometrical setting of gauge theories of the Yang–Mills type. Rev. Mod. Phys., 52, 175–197.CrossRefGoogle Scholar
[63] Dashen, R. F., Hasslacher, B. and Neveu, A. 1974. Nonperturbative methods and extended hadron models in field theory. 1. Semiclassical functional methods. Phys. Rev., D 10, 4114–4129.Google Scholar
[64] David, F. 1991. Phases of the large N matrix model and non-perturbative effects in 2-D gravity. Nucl. Phys., B 348, 507–524.CrossRefGoogle Scholar
[65] David, F. 1993. Non-perturbative effects in matrix models and vacua of twodimensional gravity. Phys. Lett., B 302, 403–410.CrossRefGoogle Scholar
[66] Delabaere, E., Dillinger, H. and Pham, F. 1997. Exact semiclassical expansions for one-dimensional quantum oscillators. J. Math. Phys., 38, 6126–6184.CrossRefGoogle Scholar
[67] Del Debbio, L., Giusti, L. and Pica, C. 2005. Topological susceptibility in the SU(3) gauge theory. Phys. Rev. Lett., 94, 032003.CrossRefGoogle ScholarPubMed
[68] Di Francesco, P. 2006. 2D quantum gravity, matrix models and graph combinatorics. In: Applications of Random Matrices in Physics, E., Brézin et al. (eds.), pp. 33–88. Springer-Verlag.Google Scholar
[69] Di Francesco, P., Ginsparg, P. H. and Zinn-Justin, J. 1995. 2-D gravity and random matrices. Phys. Rep., 254, 1–133.CrossRefGoogle Scholar
[70] Dingle, R. B. 1973. Asymptotic Expansions: their Derivation and Interpretation. Academic Press.Google Scholar
[71] Di Vecchia, P. 1979. An effective Lagrangian with no U(1) problem in ℂℙn−1 models and QCD. Phys. Lett., B 85, 357–360.CrossRefGoogle Scholar
[72] Di Vecchia, P. and Veneziano, G. 1980. Chiral dynamics in the large n limit. Nucl. Phys., B 171, 253–272.CrossRefGoogle Scholar
[73] Donaldson, S. K. and Kronheimer, P. B. 1990. The Geometry of Four-Manifolds. Oxford University Press.Google Scholar
[74] Donoghue, J. F., Golwich, E. and Holstein, B. R. 1994. Dynamics of the Standard Model. Cambridge University Press.Google Scholar
[75] Dorey, N., Hollowood, T. J., Khoze, V. V. and Mattis, M. P. 2002. The calculus of many instantons. Phys. Rep., 371, 231–459.CrossRefGoogle Scholar
[76] Dorigoni, D. 2014. An introduction to resurgence, trans-series and alien calculus. arXiv:1411.3585 [hep-th].
[77] Dunne, G. V. 2002. Perturbative–nonperturbative connection in quantum mechanics and field theory. In: Continuous Advances in QCD, K. A., Olive et al. (eds.), pp. 478– 505. World Scientific.Google Scholar
[78] Dunne, G. V. 2008. Functional determinants in quantum field theory. J. Phys. A: Math. Theor., 41, 304006.CrossRefGoogle Scholar
[79] Dunne, G. V. and Min, H. 2005. Beyond the thin-wall approximation: precise numerical computation of prefactors in false vacuum decay. Phys. Rev., D 72, 125004.Google Scholar
[80] Dunne, G. V. and Unsal, M. 2012. Resurgence and trans-series in quantum field theory: the ℂℙN−1 model. JHEP, 1211, 170.CrossRefGoogle Scholar
[81] Dunne, G. V. and Unsal, M. 2014. Uniform WKB, multi-instantons, and resurgent trans-series. Phys. Rev., D 89, 105009.Google Scholar
[82] Dyson, F. J. 1952. Divergence of perturbation theory in quantum electrodynamics. Phys. Rev., 85, 631–632.CrossRefGoogle Scholar
[83] Einhorn, M. B. and Wudka, J. 2003. On the Vafa–Witten theorem on spontaneous breaking of parity. Phys. Rev., D 67, 045004.Google Scholar
[84] Eynard, B. 2004. Topological expansion for the 1-Hermitian matrix model correlation functions. JHEP, 0411, 031.CrossRefGoogle Scholar
[85] Eynard, B. and Orantin, N. 2007. Invariants of algebraic curves and topological expansion. Commun. Num. Theor. Phys., 1, 347–452.CrossRefGoogle Scholar
[86] Feynman, R. P. 1998. Statistical Mechanics. Westview Press.Google Scholar
[87] Forrester, P. J. 2010. Log-Gases and Random Matrices. Princeton University Press.Google Scholar
[88] Forrester, P. J. and Warnaar, S. O. 2008. The importance of the Selberg integral. Bull. Am. Math. Soc. (N.S.), 45, 489–534.CrossRefGoogle Scholar
[89] Frishman, Y. and Sonnenschein, J. 2010. Non-Perturbative Field Theory. Cambridge University Press.CrossRef
[90] Fujikawa, K. 1980. Path integral for gauge theories with fermions. Phys. Rev., D 21, 2848–2858.Google Scholar
[91] Fujikawa, K. and Suzuki, H. 2004. Path Integrals and Quantum Anomalies. Oxford University Press.CrossRefGoogle Scholar
[92] Gasser, J. and Leutwyler, H. 1984. Chiral perturbation theory to one loop. Ann. Phys., 158, 142–210.CrossRefGoogle Scholar
[93] Gibbons, G. W. and Hawking, S. W. 1977. Action integrals and partition functions in quantum gravity. Phys. Rev., D 15, 2752–2756.Google Scholar
[94] Ginsparg, P. H. and Moore, G. W. 1993. Lectures on 2-D gravity and 2-D string theory. hep-th/9304011.
[95] Ginsparg, P. H. and Zinn-Justin, J. 1990. 2-d gravity + 1-d matter. Phys. Lett., B 240, 333–340.CrossRefGoogle Scholar
[96] Giusti, L., Rossi, G. C. and Veneziano, G. 2002. The UA(1) problem on the lattice with Ginsparg–Wilson fermions. Nucl. Phys., B 628, 234–252.CrossRefGoogle Scholar
[97] Giusti, L., Rossi, G. C. and Testa, M. 2004. Topological susceptibility in full QCD with Ginsparg–Wilson fermions. Phys. Lett., B 587, 157–166.CrossRefGoogle Scholar
[98] Giusti, L., Petrarca, S. and Taglienti, B. 2007. Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice. Phys. Rev., D 76, 094510.Google Scholar
[99] Gopakumar, R. 1996. The master field revisited. Nucl. Phys. Proc. Suppl., 45B, 244–250.Google Scholar
[100] Graffi, S., Grecchi, V. and Simon, B. 1970. Borel summability: application to the anharmonic oscillator. Phys. Lett., B 32, 631–634.CrossRefGoogle Scholar
[101] Gross, D. J. and Matytsin, A. 1994. Instanton induced large N phase transitions in two-dimensional and four-dimensional QCD. Nucl. Phys., B 429, 50–74.CrossRefGoogle Scholar
[102] Gross, D. J. and Witten, E. 1980. Possible third order phase transition in the large N lattice gauge theory. Phys. Rev., D 21, 446–453.Google Scholar
[103] Gross, D. J., Pisarski, R. D. and Yaffe, L. G. 1981. QCD and instantons at finite temperature. Rev. Mod. Phys., 53, 43–80.CrossRefGoogle Scholar
[104] Gross, D. J., Perry, M. J. and Yaffe, L. G. 1982. Instability of flat space at finite temperature. Phys. Rev., D 25, 330–355.Google Scholar
[105] Grunberg, G. 1994. Perturbation theory and condensates. Phys. Lett., B 325, 441–448.CrossRefGoogle Scholar
[106] Herbst, I. W. and Simon, B. 1978. Some remarkable examples in eigenvalue perturbation theory. Phys. Lett., B 78, 304–306.CrossRefGoogle Scholar
[107] Herrera-Siklody, P., Latorre, J. I., Pascual, P. and Taron, J. 1997. Chiral effective Lagrangian in the large N(c) limit: the nonet case. Nucl. Phys., B 497, 345–386.CrossRefGoogle Scholar
[108] Huang, S., Negele, J. W. and Polonyi, J. 1988. Meson structure in QCD in twodimensions. Nucl. Phys., B 307, 669–704.CrossRefGoogle Scholar
[109] Jack, I. and Osborn, H. 1984. Background field calculations in curved space-time. 1. General formalism and application to scalar fields. Nucl. Phys., B 234, 331–364.CrossRefGoogle Scholar
[110] Jackiw, R. 1977. Quantum meaning of classical field theory. Rev. Mod. Phys., 49, 681–706.CrossRefGoogle Scholar
[111] Jackiw, R. 1985. Topological investigations of quantized gauge theories. In: Current Algebra and Anomalies, S. B., Treiman, R., Jackiw, B., Zumino and E, Witten (eds.), pp. 240–360. World Scientific.Google Scholar
[112] Jackiw, R. and Rebbi, C. 1976. Vacuum periodicity in a Yang–Mills quantum theory. Phys. Rev. Lett., 37, 172–175.CrossRefGoogle Scholar
[113] Jafarizadeh, M. A. and Fakhri, H. 1997. Calculation of the determinant of shape invariant operators. Phys. Lett., A 230, 157–163.CrossRefGoogle Scholar
[114] Jentschura, U. D. and Zinn-Justin, J. 2011. Multi-instantons and exact results. IV: Path integral formalism. Ann. Phys., 326, 2186–2242.CrossRefGoogle Scholar
[115] Jentschura, U. D., Surzhykov, A. and Zinn-Justin, J. 2010. Multi-instantons and exact results. III: Unification of even and odd anharmonic oscillators. Ann. Phys., 325, 1135–1172.CrossRefGoogle Scholar
[116] Jurkiewicz, J. and Zalewski, K. 1983. Vacuum structure of the U(N → infinity) gauge theory on a two-dimensional lattice for a broad class of variant actions. Nucl. Phys., B 220, 167–184.CrossRefGoogle Scholar
[117] Kalashnikova, Y. S. and Nefediev, A. V. 2002. Two-dimensional QCD in the Coulomb gauge. Phys. Usp., 45, 347–368.CrossRefGoogle Scholar
[118] Kalashnikova, Y. S., Nefediev, A. V. and Volodin, A. V. 2000. Hamiltonian approach to the bound state problem in QCD2. Phys. Atom. Nucl., 63, 1623–1628.CrossRefGoogle Scholar
[119] Kaul, R. K. and Rajaraman, R. 1983. Soliton energies in supersymmetric theories. Phys. Lett., B 131, 357–361.CrossRefGoogle Scholar
[120] Konishi, K. and Paffuti, G. 2009. Quantum Mechanics. A New Introduction. Oxford University Press.Google Scholar
[121] Koplik, J., Neveu, A. and Nussinov, S. 1977. Some aspects of the planar perturbation series. Nucl. Phys., B 123, 109–131.CrossRefGoogle Scholar
[122] Le Guillou, J. C. and Zinn-Justin, J. (eds.) 1990. Large Order Behavior of Perturbation Theory. North-Holland.Google Scholar
[123] Lenz, F., Thies, M., Yazaki, K. and Levit, S. 1991. Hamiltonian formulation of two-dimensional gauge theories on the light cone. Ann. Phys., 208, 1–89.CrossRefGoogle Scholar
[124] Li, M., Wilets, M. and Birse, M. C. 1987. QCD In two-dimensions in the axial gauge. J. Phys., G 13, 915–923.CrossRefGoogle Scholar
[125] Lipatov, L. N. 1977. Divergence of the perturbation theory series and the quasiclassical theory. Sov. Phys. JETP, 45, 216–223.Google Scholar
[126] Lucini, B. and Panero, M. 2013. SU(N) gauge theories at large N. Phys. Rep., 526, 93–163.CrossRefGoogle Scholar
[127] Lüscher, M. 1982. Dimensional regularization in the presence of large background fields. Ann. Phys., 142, 359–392.CrossRefGoogle Scholar
[128] Lüscher, M. 1982. A semiclassical formula for the topological susceptibility in a finite space-time volume. Nucl. Phys., B 205, 483–503.CrossRefGoogle Scholar
[129] Lüscher, M. 2004. Topological effects in QCD and the problem of short-distance singularities. Phys. Lett., B 593, 296–301.CrossRefGoogle Scholar
[130] Lüscher, M. 2010. Properties and uses of the Wilson flow in lattice QCD. JHEP, 1008, 071.CrossRefGoogle Scholar
[131] Lüscher, M. and Palombi, F. 2010. Universality of the topological susceptibility in the SU(3) gauge theory. JHEP, 1009, 110.CrossRefGoogle Scholar
[132] Majumdar, S. N. and Schehr, G. 2014. Top eigenvalue of a random matrix: large deviations and third order phase transitions. J. Stat. Mech., P01012.CrossRefGoogle Scholar
[133] Majumdar, S. N. and Vergassola, M. 2009. Large deviations of the maximum eigenvalue for Wishart and Gaussian random matrices. Phys. Rev. Lett., 102, 060601.CrossRefGoogle ScholarPubMed
[134] Manohar, A. V. 1998. Large N QCD. arXiv:hep-ph/9802419.
[135] Mariño, M. 2004. Les Houches lectures on matrix models and topological strings. hep-th/0410165.
[136] Mariño, M. 2008. Nonperturbative effects and nonperturbative definitions in matrix models and topological strings. JHEP, 0812, 114.CrossRefGoogle Scholar
[137] Mariño, M. 2014. Lectures on non-perturbative effects in large N gauge theories, matrix models and strings. Fortschr. Phys., 62, 455–540.CrossRefGoogle Scholar
[138] Mariño, M. and Putrov, P. 2009. Multi-instantons in large N matrix quantum mechanics. arXiv:0911.3076 [hep-th].
[139] Mariño, M., Schiappa, R. and Weiss, M. 2008. Non-perturbative effects and the large-order behavior of matrix models and topological strings. Commun. Num. Theor. Phys., 2, 349–419.CrossRefGoogle Scholar
[140] McKane, A. J. and Tarlie, M. B. 1995. Regularisation of functional determinants using boundary perturbations. J. Phys., A 28, 6931–6942.Google Scholar
[141] Meggiolaro, E. 1998. The topological susceptibility of QCD: from Minkowskian to Euclidean theory. Phys. Rev., D 58, 085002.Google Scholar
[142] Mehta, M. L. 2004. Random Matrices. Elsevier.Google Scholar
[143] Miller, P. 2006. Applied Asymptotic Analysis. American Mathematical Society.CrossRefGoogle Scholar
[144] Münster, G. 1982. The 1/N expansion and instantons in ℂℙN−1 models on a sphere. Phys. Lett., B 118, 380–384.CrossRefGoogle Scholar
[145] Münster, G. 1983. A study of ℂℙN−1 models on the sphere within the 1/N expansion. Nucl. Phys., B 218, 1–31.CrossRefGoogle Scholar
[146] Negele, J. W. 1982. The mean-field theory of nuclear structure and dynamics. Rev. Mod. Phys., 54, 913–1015.CrossRefGoogle Scholar
[147] Negele, J. W. and Orland, H. 1998. Quantum Many-Particle Systems. Westview Press.Google Scholar
[148] Nepomechie, R. I. 1985. Calculating heat kernels. Phys. Rev., D 31, 3291–3292.Google ScholarPubMed
[149] Neuberger, H. 1980. Instantons as a bridgehead at N = infinity. Phys. Lett., B 94, 199–202.CrossRefGoogle Scholar
[150] Neuberger, H. 1981. Nonperturbative contributions in models with a nonanalytic behavior at infinite N. Nucl. Phys., B 179, 253–282.CrossRefGoogle Scholar
[151] Osborn, H. 1981. Semiclassical functional integrals for selfdual gauge fields. Ann. Phys., 135, 373–415.CrossRefGoogle Scholar
[152] Parisi, G. 1978. Singularities of the borel transform in renormalizable theories. Phys. Lett., B 76, 65–66.CrossRefGoogle Scholar
[153] Perelomov, A. M. 1987. Chiral models: geometrical aspects. Phys. Rep., 146, 135–213.CrossRefGoogle Scholar
[154] Peskin, M. E. and Schroeder, D. V. 1995. An Introduction to Quantum Field Theory. Addison-Wesley.Google Scholar
[155] Polyakov, A. M. 1977. Quark confinement and topology of gauge groups. Nucl. Phys., B 120, 429–458.CrossRefGoogle Scholar
[156] Polyakov, A. M. 1987. Gauge Fields and Strings. Harwood Academic Publishers.Google Scholar
[157] Rajaraman, R. 1982. Solitons and Instantons. North-Holland.Google Scholar
[158] Ramond, P. 2001. Field Theory. A Modern Primer, second edition. Westview Press.Google Scholar
[159] Salomonson, P. and van Holten, J. W. 1982. Fermionic coordinates and supersymmetry in quantum mechanics. Nucl. Phys., B 196, 509–531.CrossRefGoogle Scholar
[160] Schafer, T. and Shuryak, E. V. 1998. Instantons in QCD. Rev. Mod. Phys., 70, 323–426.CrossRefGoogle Scholar
[161] Schwab, P. 1982. Semiclassical approximation for the topological susceptibility in ℂℙN−1 models on a sphere. Phys. Lett., B 118, 373–379.CrossRefGoogle Scholar
[162] Schwab, P. 1983. Two instanton contribution to the topological susceptibility in ℂℙN−1 models on a sphere. Phys. Lett., B 126, 241–246.CrossRefGoogle Scholar
[163] Schwarz, A. S. 1979. Instantons and fermions in the field of instanton. Commun. Math. Phys., 64, 233–268.CrossRefGoogle Scholar
[164] Seara, T. M. and Sauzin, D. 2003. Ressumació de Borel i teoria de la ressurgència. Bull. Soc. Catlana Mat., 18, 131–153.Google Scholar
[165] Seiler, E. 2002. Some more remarks on the Witten–Veneziano formula for the etaprime mass. Phys. Lett., B 525, 355–359.CrossRefGoogle Scholar
[166] Shenker, S. H. 1992. The strength of nonperturbative effects in string theory. In: Random Surfaces and Quantum Gravity, O., Álvarez, E., Marinari and P., Windey (eds.), pp. 191–200. Plenum Press.Google Scholar
[167] Shifman, M. 2012. Advanced Topics in Quantum Field Theory. Cambridge University Press,Google Scholar
[168] Shore, G. M. 1979. Dimensional regularization and instantons. Ann. Phys., 122, 321–372.CrossRefGoogle Scholar
[169] Simon, B. 1982. Large orders and summability of eigenvalue perturbation theory: a mathematical overview. Int. J. Quant. Chem., 21, 3–25.CrossRefGoogle Scholar
[170] Stone, M. 1977. Semiclassical methods for unstable states. Phys. Lett., B 67, 186–188.CrossRefGoogle Scholar
[171] Stone, M. and Reeve, J. 1978. Late terms in the asymptotic expansion for the energy levels of a periodic potential. Phys. Rev., D 18, 4746–4751.Google Scholar
[172] Takhtajan, L. 2008. Quantum Mechanics for Mathematicians. American Mathematical Society.CrossRefGoogle Scholar
[173] 't Hooft, G. 1974. A planar diagram theory for strong interactions. Nucl. Phys., B 72, 461–473.CrossRefGoogle Scholar
[174] 't Hooft, G. 1974. A two-dimensional model for mesons. Nucl. Phys., B 75, 461–470.CrossRefGoogle Scholar
[175] 't Hooft, G. 1976. Computation of the quantum effects due to a four-dimensional pseudoparticle. Phys. Rev., D 14, 3432–3450.Google Scholar
[176] Tong, D. 2005. TASI lectures on solitons: instantons, monopoles, vortices and kinks. hep-th/0509216.
[177] Vafa, C. and Witten, E. 1984. Parity conservation in QCD. Phys. Rev. Lett., 53, 535–536.CrossRefGoogle Scholar
[178] Vandoren, S. and van Nieuwenhuizen, P. 2008. Lectures on instantons. arXiv:0802.1862 [hep-th].
[179] Vassilevich, D. V. 2003. Heat kernel expansion: user's manual. Phys. Rep., 388, 279–360.CrossRefGoogle Scholar
[180] Veneziano, G. 1979. U(1) without instantons. Nucl. Phys., B 159, 213–224.CrossRefGoogle Scholar
[181] Vicari, E. 1999. The Euclidean two point correlation function of the topological charge density. Nucl. Phys., B 554, 301–312.CrossRefGoogle Scholar
[182] Vicari, E. and Panagopoulos, H. 2009. Theta dependence of SU(N) gauge theories in the presence of a topological term. Phys. Rep., 470, 93–150.CrossRefGoogle Scholar
[183] Wadia, S. R. 1979. A study of U(N) lattice gauge theory in 2-dimensions. EFI-79/44-CHICAGO, arXiv:1212.2906 [hep-th].
[184] Wadia, S. R. 1980. N = infinity phase transition in a class of exactly soluble model lattice gauge theories. Phys. Lett., B 93, 403–410.CrossRefGoogle Scholar
[185] Weinberg, S. 1975. The U(1) problem. Phys. Rev., D 11, 3583–3593.Google Scholar
[186] Weinberg, S. 1996. The Quantum Theory of Fields. Volume II: Modern Applications. Cambridge University Press.CrossRefGoogle Scholar
[187] Witten, E. 1979. Instantons, the quark model, and the 1/N expansion. Nucl. Phys., B 149, 285–320.CrossRefGoogle Scholar
[188] Witten, E. 1979. Current algebra theorems for the U(1) goldstone boson. Nucl. Phys., B 156, 269–283.CrossRefGoogle Scholar
[189] Witten, E. 1979. Baryons in the 1/N expansion. Nucl. Phys., B 160, 57–115.CrossRefGoogle Scholar
[190] Witten, E. 1980. The 1/N expansion in atomic and particle physics. In: Recent Developments in Gauge Theories, G., 't Hooft et al. (eds.), pp. 403–419. Plenum Press.
[191] Witten, E. 1980. Quarks, atoms, and the 1/N expansion. Phys. Today, 33, 38–43.CrossRefGoogle Scholar
[192] Witten, E. 1980. Large N chiral dynamics. Ann. Phys., 128, 363–375.CrossRefGoogle Scholar
[193] Witten, E. 1981. Dynamical breaking of supersymmetry. Nucl. Phys., B 188, 513–554.CrossRefGoogle Scholar
[194] Witten, E. 1982. Instability of the Kaluza–Klein vacuum. Nucl. Phys., B 195, 481–492.CrossRefGoogle Scholar
[195] Witten, E. 1998. Theta dependence in the large N limit of four-dimensional gauge theories. Phys. Rev. Lett., 81, 2862–2865.CrossRefGoogle Scholar
[196] Yaris, R., Bendler, J., Lovett, R., Bender, C. M. and Fedders, P. A. 1978. Resonance calculations for arbitrary potentials. Phys. Rev., A 18, 1816–1825.CrossRefGoogle Scholar
[197] Ynduráin, F. J. 2006. The Theory of Quark and Gluon Interactions. Springer-Verlag.Google Scholar
[198] Zinn-Justin, J. 1983. Multi-instanton contributions in quantum mechanics. 2. Nucl. Phys., B 218, 333–348.CrossRefGoogle Scholar
[199] Zinn-Justin, J. 2002. Quantum Field Theory and Critical Phenomena. Oxford University Press.CrossRefGoogle Scholar
[200] Zinn-Justin, J. and Jentschura, U. D. 2004. Multi-instantons and exact results I: conjectures, WKB expansions, and instanton interactions. Ann. Phys., 313, 197–267.CrossRefGoogle Scholar
[201] Zinn-Justin, J. and Jentschura, U. D. 2004. Multi-instantons and exact results II: specific cases, higher-order effects, and numerical calculations. Ann. Phys., 313, 269–325.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Marcos Mariño, Université de Genève
  • Book: Instantons and Large N
  • Online publication: 05 September 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781107705968.015
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Marcos Mariño, Université de Genève
  • Book: Instantons and Large N
  • Online publication: 05 September 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781107705968.015
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Marcos Mariño, Université de Genève
  • Book: Instantons and Large N
  • Online publication: 05 September 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781107705968.015
Available formats
×