Abstract
A black hole described in SU(N ) gauge theory consists of N D-branes. By separating one of the D-branes from others and studying the interaction between them, the black hole geometry can be probed. In order to obtain quantitative results, we employ the lattice Monte Carlo simulation. As a proof of the concept, we perform an explicit calculation in the matrix model dual to the black zero-brane in type IIA string theory. We demonstrate this method actually works in the high temperature region, where the stringy correction is large. We argue possible dual gravity interpretations.
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References
T. Eguchi and H. Kawai, Reduction of Dynamical Degrees of Freedom in the Large-N Gauge Theory, Phys. Rev. Lett. 48 (1982) 1063 [INSPIRE].
G. Bhanot, U.M. Heller and H. Neuberger, The Quenched Eguchi-Kawai Model, Phys. Lett. B 113 (1982) 47 [INSPIRE].
D.J. Gross and Y. Kitazawa, A Quenched Momentum Prescription for Large-N Theories, Nucl. Phys. B 206 (1982) 440 [INSPIRE].
G. Parisi, A Simple Expression for Planar Field Theories, Phys. Lett. B 112 (1982) 463 [INSPIRE].
A. Gonzalez-Arroyo and M. Okawa, The Twisted Eguchi-Kawai Model: A Reduced Model for Large-N Lattice Gauge Theory, Phys. Rev. D 27 (1983) 2397 [INSPIRE].
E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].
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].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, Bulk and Transhorizon Measurements in AdS/CFT, JHEP 10 (2012) 165 [arXiv:1201.3664] [INSPIRE].
B. de Wit, J. Hoppe and H. Nicolai, On the Quantum Mechanics of Supermembranes, Nucl. Phys. B 305 (1988) 545 [INSPIRE].
J.M. Maldacena, Probing near extremal black holes with D-branes, Phys. Rev. D 57 (1998) 3736 [hep-th/9705053] [INSPIRE].
A.A. Tseytlin and S. Yankielowicz, Free energy of N = 4 super Yang-Mills in Higgs phase and nonextremal D3-brane interactions, Nucl. Phys. B 541 (1999) 145 [hep-th/9809032] [INSPIRE].
N. Dorey, T.J. Hollowood, V.V. Khoze, M.P. Mattis and S. Vandoren, Multi-instanton calculus and the AdS/CFT correspondence in N = 4 superconformal field theory, Nucl. Phys. B 552 (1999) 88 [hep-th/9901128] [INSPIRE].
I.L. Buchbinder, A. Yu. Petrov and A.A. Tseytlin, Two loop N = 4 super Yang-Mills effective action and interaction between D3-branes, Nucl. Phys. B 621 (2002) 179 [hep-th/0110173] [INSPIRE].
N. Iizuka, D.N. Kabat, G. Lifschytz and D.A. Lowe, Probing black holes in nonperturbative gauge theory, Phys. Rev. D 65 (2002) 024012 [hep-th/0108006] [INSPIRE].
S.M. Kuzenko, Self-dual effective action of N = 4 SYM revisited, JHEP 03 (2005) 008 [hep-th/0410128] [INSPIRE].
F. Ferrari, Emergent Space and the Example of AdS 5 XS 5, Nucl. Phys. B 869 (2013) 31 [arXiv:1207.0886] [INSPIRE].
F. Ferrari, D-Brane Probes in the Matrix Model, Nucl. Phys. B 880 (2014) 290 [arXiv:1311.4520] [INSPIRE].
I.L. Buchbinder, E.A. Ivanov and I.B. Samsonov, The low-energy N = 4 SYM effective action in diverse harmonic superspaces, Phys. Part. Nucl. 48 (2017) 333 [arXiv:1603.02768] [INSPIRE].
J.H. Schwarz, Gauge Theories on the Coulomb branch, Subnucl. Ser. 52 (2017) 167 [arXiv:1408.0852] [INSPIRE].
V. Sahakian, Y. Tawabutr and C. Yan, Emergent spacetime & quantum entanglement in matrix theory, JHEP 08 (2017) 140 [arXiv:1705.01128] [INSPIRE].
A. Mollabashi, N. Shiba and T. Takayanagi, Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy, JHEP 04 (2014) 185 [arXiv:1403.1393] [INSPIRE].
A. Karch and C.F. Uhlemann, Holographic entanglement entropy and the internal space, Phys. Rev. D 91 (2015) 086005 [arXiv:1501.00003] [INSPIRE].
D. Berenstein and E. Dzienkowski, Numerical Evidence for Firewalls, arXiv:1311.1168 [INSPIRE].
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].
E. Berkowitz, M. Hanada and J. Maltz, Chaos in Matrix Models and Black Hole Evaporation, Phys. Rev. D 94 (2016) 126009 [arXiv:1602.01473] [INSPIRE].
E. Berkowitz, M. Hanada and J. Maltz, A microscopic description of black hole evaporation via holography, Int. J. Mod. Phys. D 25 (2016) 1644002 [arXiv:1603.03055] [INSPIRE].
F. Ferrari, Black Hole Horizons and Bose-Einstein Condensation, arXiv:1601.08120 [INSPIRE].
L. Kofman, A.D. Linde, X. Liu, A. Maloney, L. McAllister and E. Silverstein, Beauty is attractive: Moduli trapping at enhanced symmetry points, JHEP 05 (2004) 030 [hep-th/0403001] [INSPIRE].
U.H. Danielsson, G. Ferretti and B. Sundborg, D particle dynamics and bound states, Int. J. Mod. Phys. A 11 (1996) 5463 [hep-th/9603081] [INSPIRE].
D.N. Kabat and P. Pouliot, A Comment on zero-brane quantum mechanics, Phys. Rev. Lett. 77 (1996) 1004 [hep-th/9603127] [INSPIRE].
M. Hanada, A simulation code prepared for the Monte Carlo String/M-theory Collaboration, downloadable at https://sites.google.com/site/hanadamasanori/home/mmmm.
T. Azeyanagi, M. Hanada, T. Hirata and H. Shimada, On the shape of a D-brane bound state and its topology change, JHEP 03 (2009) 121 [arXiv:0901.4073] [INSPIRE].
M. Berkooz and M.R. Douglas, Five-branes in M(atrix) theory, Phys. Lett. B 395 (1997) 196 [hep-th/9610236] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
V.G. Filev and D. O’Connor, A Computer Test of Holographic Flavour Dynamics, JHEP 05 (2016) 122 [arXiv:1512.02536] [INSPIRE].
Y. Asano, V.G. Filev, S. Kováčik and D. O’Connor, The flavoured BFSS model at high temperature, JHEP 01 (2017) 113 [arXiv:1605.05597] [INSPIRE].
Y. Asano, V.G. Filev, S. Kováčik and D. O’Connor, A Computer Test of Holographic Flavour Dynamics II, arXiv:1612.09281 [INSPIRE].
J. Babington, J. Erdmenger, N.J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in nonsupersymmetric gauge / gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [INSPIRE].
C. Hoyos-Badajoz, K. Landsteiner and S. Montero, Holographic meson melting, JHEP 04 (2007) 031 [hep-th/0612169] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [INSPIRE].
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].
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].
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].
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].
M. Hanada, Y. Hyakutake, G. Ishiki and J. Nishimura, Holographic description of quantum black hole on a computer, Science 344 (2014) 882 [arXiv:1311.5607] [INSPIRE].
D. Kadoh and S. Kamata, Gauge/gravity duality and lattice simulations of one dimensional SYM with sixteen supercharges, arXiv:1503.08499 [INSPIRE].
M. Hanada, Y. Hyakutake, G. Ishiki and J. Nishimura, Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finite N, Phys. Rev. D 94 (2016) 086010 [arXiv:1603.00538] [INSPIRE].
E. Berkowitz, E. Rinaldi, M. Hanada, G. Ishiki, S. Shimasaki and P. Vranas, Precision lattice test of the gauge/gravity duality at large-N , Phys. Rev. D 94 (2016) 094501 [arXiv:1606.04951] [INSPIRE].
Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
Y. Hyakutake, Quantum near-horizon geometry of a black 0-brane, PTEP 2014 (2014) 033B04 [arXiv:1311.7526] [INSPIRE].
S.D. Mathur, The Fuzzball proposal for black holes: An Elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
M. Hanada and J. Maltz, A proposal of the gauge theory description of the small Schwarzschild black hole in AdS 5×S 5, JHEP 02 (2017) 012 [arXiv:1608.03276] [INSPIRE].
T. Banks, W. Fischler, I.R. Klebanov and L. Susskind, Schwarzschild black holes from matrix theory, Phys. Rev. Lett. 80 (1998) 226 [hep-th/9709091] [INSPIRE].
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Rinaldi, E., Berkowitz, E., Hanada, M. et al. Toward holographic reconstruction of bulk geometry from lattice simulations. J. High Energ. Phys. 2018, 42 (2018). https://doi.org/10.1007/JHEP02(2018)042
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DOI: https://doi.org/10.1007/JHEP02(2018)042