Matrix thermalization. (English) Zbl 1377.83063

Summary: Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.


83C80 Analogues of general relativity in lower dimensions
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81S10 Geometry and quantization, symplectic methods


Full Text: DOI arXiv


[1] Y.V. Kovchegov and A. Taliotis, Early time dynamics in heavy ion collisions from AdS/CFT correspondence, Phys. Rev.C 76 (2007) 014905 [arXiv:0705.1234] [INSPIRE].
[2] J.L. Albacete, Y.V. Kovchegov and A. Taliotis, Modeling heavy ion collisions in AdS/CFT, JHEP07 (2008) 100 [arXiv:0805.2927] [INSPIRE].
[3] P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett.102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].
[4] G. Beuf, M.P. Heller, R.A. Janik and R. Peschanski, Boost-invariant early time dynamics from AdS/CFT, JHEP10 (2009) 043 [arXiv:0906.4423] [INSPIRE].
[5] J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic evolution of entanglement entropy, JHEP11 (2010) 149 [arXiv:1006.4090] [INSPIRE]. · Zbl 1294.81128
[6] T. Albash and C.V. Johnson, Evolution of holographic entanglement entropy after thermal and electromagnetic quenches, New J. Phys.13 (2011) 045017 [arXiv:1008.3027] [INSPIRE]. · Zbl 1448.83015
[7] V. Balasubramanian et al., Thermalization of strongly coupled field theories, Phys. Rev. Lett.106 (2011) 191601 [arXiv:1012.4753] [INSPIRE].
[8] M.P. Heller, R.A. Janik and P. Witaszczyk, The characteristics of thermalization of boost-invariant plasma from holography, Phys. Rev. Lett.108 (2012) 201602 [arXiv:1103.3452] [INSPIRE].
[9] M.P. Heller, D. Mateos, W. van der Schee and D. Trancanelli, Strong coupling isotropization of non-Abelian plasmas simplified, Phys. Rev. Lett.108 (2012) 191601 [arXiv:1202.0981] [INSPIRE].
[10] V. Balasubramanian et al., Inhomogeneous thermalization in strongly coupled field theories, Phys. Rev. Lett.111 (2013) 231602 [arXiv:1307.1487] [INSPIRE].
[11] S. Lin and E. Shuryak, Toward the AdS/CFT gravity dual for high energy collisions. III. Gravitationally collapsing shell and quasiequilibrium, Phys. Rev.D 78 (2008) 125018 [arXiv:0808.0910] [INSPIRE]. · Zbl 1080.81602
[12] V. Balasubramanian, A. Bernamonti, N. Copland, B. Craps and F. Galli, Thermalization of mutual and tripartite information in strongly coupled two dimensional conformal field theories, Phys. Rev.D 84 (2011) 105017 [arXiv:1110.0488] [INSPIRE].
[13] H. Liu and S.J. Suh, Entanglement tsunami: universal scaling in holographic thermalization, Phys. Rev. Lett.112 (2014) 011601 [arXiv:1305.7244] [INSPIRE].
[14] C.T. Asplund, A. Bernamonti, F. Galli and T. Hartman, Entanglement scrambling in 2d conformal field theory, JHEP09 (2015) 110 [arXiv:1506.03772] [INSPIRE]. · Zbl 1388.83165
[15] B. de Wit, J. Hoppe and H. Nicolai, On the quantum mechanics of supermembranes, Nucl. Phys.B 305 (1988) 545 [INSPIRE]. · Zbl 1156.81457
[16] T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev.D 55 (1997) 5112 [hep-th/9610043] [INSPIRE]. · Zbl 1156.81433
[17] J. Polchinski, M-theory and the light cone, Prog. Theor. Phys. Suppl.134 (1999) 158 [hep-th/9903165] [INSPIRE].
[18] N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large N limit of theories with sixteen supercharges, Phys. Rev.D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
[19] Y. Sekino and T. Yoneya, Generalized AdS-CFT correspondence for matrix theory in the large-N limit, Nucl. Phys.B 570 (2000) 174 [hep-th/9907029] [INSPIRE]. · Zbl 0951.81057
[20] T. Wiseman and B. Withers, Holographic renormalization for coincident Dp-branes, JHEP10 (2008) 037 [arXiv:0807.0755] [INSPIRE]. · Zbl 1245.81230
[21] I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP09 (2008) 094 [arXiv:0807.3324] [INSPIRE]. · Zbl 1245.81187
[22] Y. Sekino and L. Susskind, Fast scramblers, JHEP10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
[23] K.N. Anagnostopoulos, M. Hanada, J. Nishimura and S. Takeuchi, Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature, Phys. Rev. Lett.100 (2008) 021601 [arXiv:0707.4454] [INSPIRE].
[24] S. Catterall and T. Wiseman, Black hole thermodynamics from simulations of lattice Yang-Mills theory, Phys. Rev.D 78 (2008) 041502 [arXiv:0803.4273] [INSPIRE].
[25] M. Hanada, Y. Hyakutake, J. Nishimura and S. Takeuchi, Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics, Phys. Rev. Lett.102 (2009) 191602 [arXiv:0811.3102] [INSPIRE].
[26] S. Catterall and T. Wiseman, Extracting black hole physics from the lattice, JHEP04 (2010) 077 [arXiv:0909.4947] [INSPIRE]. · Zbl 1272.83046
[27] D. Kadoh and S. Kamata, Gauge/gravity duality and lattice simulations of one dimensional SYM with sixteen supercharges, arXiv:1503.08499 [INSPIRE].
[28] V.G. Filev and D. O’Connor, The BFSS model on the lattice, JHEP05 (2016) 167 [arXiv:1506.01366] [INSPIRE].
[29] A.V. Smilga, Comments on thermodynamics of supersymmetric matrix models, Nucl. Phys.B 818 (2009) 101 [arXiv:0812.4753] [INSPIRE]. · Zbl 1194.81218
[30] T. Wiseman, On black hole thermodynamics from super Yang-Mills, JHEP07 (2013) 101 [arXiv:1304.3938] [INSPIRE]. · Zbl 1342.83435
[31] T. Morita, S. Shiba, T. Wiseman and B. Withers, Warm p-soup and near extremal black holes, Class. Quant. Grav.31 (2014) 085001 [arXiv:1311.6540] [INSPIRE]. · Zbl 1291.81336
[32] T. Morita, S. Shiba, T. Wiseman and B. Withers, Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N, JHEP07 (2015) 047 [arXiv:1412.3939] [INSPIRE]. · Zbl 1388.83486
[33] R. Hübener, Y. Sekino and J. Eisert, Equilibration in low-dimensional quantum matrix models, JHEP04 (2015) 166 [arXiv:1403.1392] [INSPIRE]. · Zbl 1388.81014
[34] C.T. Asplund, D. Berenstein and E. Dzienkowski, Large N classical dynamics of holographic matrix models, Phys. Rev.D 87 (2013) 084044 [arXiv:1211.3425] [INSPIRE].
[35] S. Aoki, M. Hanada and N. Iizuka, Quantum black hole formation in the BFSS matrix model, JHEP07 (2015) 029 [arXiv:1503.05562] [INSPIRE]. · Zbl 1388.83369
[36] G. Gur-Ari, M. Hanada and S.H. Shenker, Chaos in classical D0-brane mechanics, JHEP02 (2016) 091 [arXiv:1512.00019] [INSPIRE].
[37] C. Asplund, D. Berenstein and D. Trancanelli, Evidence for fast thermalization in the plane-wave matrix model, Phys. Rev. Lett.107 (2011) 171602 [arXiv:1104.5469] [INSPIRE].
[38] N. Iizuka, D. Kabat, S. Roy and D. Sarkar, Black hole formation at the correspondence point, Phys. Rev.D 87 (2013) 126010 [arXiv:1303.7278] [INSPIRE].
[39] N. Iizuka, D. Kabat, S. Roy and D. Sarkar, Black hole formation in fuzzy sphere collapse, Phys. Rev.D 88 (2013) 044019 [arXiv:1306.3256] [INSPIRE].
[40] G.T. Horowitz, N. Iqbal and J.E. Santos, Simple holographic model of nonlinear conductivity, Phys. Rev.D 88 (2013) 126002 [arXiv:1309.5088] [INSPIRE].
[41] S. Bhattacharyya and S. Minwalla, Weak field black hole formation in asymptotically AdS spacetimes, JHEP09 (2009) 034 [arXiv:0904.0464] [INSPIRE].
[42] A. Jevicki, Y. Kazama and T. Yoneya, Generalized conformal symmetry in D-brane matrix models, Phys. Rev.D 59 (1999) 066001 [hep-th/9810146] [INSPIRE].
[43] A. Jevicki and T. Yoneya, Space-time uncertainty principle and conformal symmetry in D-particle dynamics, Nucl. Phys.B 535 (1998) 335 [hep-th/9805069] [INSPIRE]. · Zbl 1080.81602
[44] T. Yoneya, Generalized conformal symmetry and oblique AdS/CFT correspondence for matrix theory, Class. Quant. Grav.17 (2000) 1307 [hep-th/9908153] [INSPIRE]. · Zbl 0952.81029
[45] A. Strominger, AdS2quantum gravity and string theory, JHEP01 (1999) 007 [hep-th/9809027] [INSPIRE]. · Zbl 0965.81097
[46] J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP02 (1999) 011 [hep-th/9812073] [INSPIRE]. · Zbl 0956.83052
[47] A. Almheiri and J. Polchinski, Models of AdS2backreaction and holography, JHEP11 (2015) 014 [arXiv:1402.6334] [INSPIRE]. · Zbl 1388.83079
[48] K. Jensen, Chaos in AdS2holography, Phys. Rev. Lett.117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
[49] J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, Prog. Theor. Exp. Phys.2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE]. · Zbl 1361.81112
[50] J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS2backreaction and holography, JHEP07 (2016) 139 [arXiv:1606.03438] [INSPIRE]. · Zbl 1390.83104
[51] D. Grumiller, J. Salzer and D. Vassilevich, Aspects of AdS2holography with non-constant dilaton, arXiv:1607.06974 [INSPIRE]. · Zbl 1386.83102
[52] M. Cvetič and I. Papadimitriou, AdS2holographic dictionary, JHEP12 (2016) 008 [arXiv:1608.07018] [INSPIRE]. · Zbl 1390.83186
[53] B.C. van Rees, Holographic renormalization for irrelevant operators and multi-trace counterterms, JHEP08 (2011) 093 [arXiv:1102.2239] [INSPIRE]. · Zbl 1298.81202
[54] K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav.19 (2002) 5849 [hep-th/0209067] [INSPIRE]. · Zbl 1044.83009
[55] T. Ortiz, H. Samtleben and D. Tsimpis, Matrix model holography, JHEP12 (2014) 096 [arXiv:1410.0487] [INSPIRE].
[56] Y. Matsuo, Y. Sasai and Y. Sekino, Linear responses of D0-branes via gauge/gravity correspondence, Phys. Rev.D 88 (2013) 026020 [arXiv:1305.2506] [INSPIRE].
[57] Y. Sekino, Supercurrents in matrix theory and the generalized AdS/CFT correspondence, Nucl. Phys.B 602 (2001) 147 [hep-th/0011122] [INSPIRE]. · Zbl 1097.81728
[58] H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP01 (1999) 003 [hep-th/9807137] [INSPIRE]. · Zbl 0965.81078
[59] K. Skenderis, Black holes and branes in string theory, Lect. Notes Phys.541 (2000) 325 [hep-th/9901050] [INSPIRE]. · Zbl 0973.83054
[60] G.T. Horowitz and A. Strominger, Black strings and P-branes, Nucl. Phys.B 360 (1991) 197 [INSPIRE].
[61] A.W. Peet and J. Polchinski, UV/IR relations in AdS dynamics, Phys. Rev.D 59 (1999) 065011 [hep-th/9809022] [INSPIRE].
[62] M. Hanada, J. Nishimura, Y. Sekino and T. Yoneya, Direct test of the gauge-gravity correspondence for matrix theory correlation functions, JHEP12 (2011) 020 [arXiv:1108.5153] [INSPIRE]. · Zbl 1306.81107
[63] W. Taylor and M. Van Raamsdonk, Multiple D0-branes in weakly curved backgrounds, Nucl. Phys.B 558 (1999) 63 [hep-th/9904095] [INSPIRE]. · Zbl 1068.81582
[64] D.N. Kabat and W. Taylor, Linearized supergravity from matrix theory, Phys. Lett.B 426 (1998) 297 [hep-th/9712185] [INSPIRE]. · Zbl 1049.83533
[65] P.G.O. Freund and M.A. Rubin, Dynamics of dimensional reduction, Phys. Lett.B 97 (1980) 233 [INSPIRE].
[66] M.J. Duncan and L.G. Jensen, Four forms and the vanishing of the cosmological constant, Nucl. Phys.B 336 (1990) 100 [INSPIRE].
[67] K. Groh, J. Louis and J. Sommerfeld, Duality and couplings of 3-form-multiplets in N = 1 supersymmetry, JHEP05 (2013) 001 [arXiv:1212.4639] [INSPIRE].
[68] D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP09 (2002) 042 [hep-th/0205051] [INSPIRE].
[69] C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP03 (2003) 046 [hep-th/0212072] [INSPIRE].
[70] K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality, Phys. Rev. Lett.101 (2008) 081601 [arXiv:0805.0150] [INSPIRE]. · Zbl 1228.81244
[71] K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality: prescription, renormalization and examples, JHEP05 (2009) 085 [arXiv:0812.2909] [INSPIRE].
[72] V. Balasubramanian et al., Thermalization of the spectral function in strongly coupled two dimensional conformal field theories, JHEP04 (2013) 069 [arXiv:1212.6066] [INSPIRE]. · Zbl 1342.81476
[73] J.R. David and S. Khetrapal, Thermalization of Green functions and quasinormal modes, JHEP07 (2015) 041 [arXiv:1504.04439] [INSPIRE]. · Zbl 1388.83219
[74] Y.-Z. Chu, TensoriaCalc package for Mathematica, http://www.stargazing.net/yizen/Tensoria.html.
[75] G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev.D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
[76] K.D. Kokkotas and B.G. Schmidt, Quasinormal modes of stars and black holes, Living Rev. Rel.2 (1999) 2 [gr-qc/9909058] [INSPIRE]. · Zbl 0984.83002
[77] R.A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: from astrophysics to string theory, Rev. Mod. Phys.83 (2011) 793 [arXiv:1102.4014] [INSPIRE].
[78] E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav.26 (2009) 163001 [arXiv:0905.2975] [INSPIRE]. · Zbl 1173.83001
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