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**Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large \(N\).**
*(English)*
Zbl 1388.83486

Summary: Maximally supersymmetric (\(p\) + 1)-dimensional Yang-Mills theory at large \(N\) and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic quantities for these strongly coupled phases, but also certain transcendental factors with a geometric origin, and allows one to deduce transitions between the phases. We emphasise it also gives predictions for the behaviour of other observables in these phases.

### MSC:

83C57 | Black holes |

83C47 | Methods of quantum field theory in general relativity and gravitational theory |

83E30 | String and superstring theories in gravitational theory |

### Keywords:

black holes in string theory; brane dynamics in gauge theories; gauge-gravity correspondence
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\textit{T. Morita} et al., J. High Energy Phys. 2015, No. 7, Paper No. 47, 55 p. (2015; Zbl 1388.83486)

### References:

[1] | J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE]. · Zbl 0969.81047 |

[2] | 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]. |

[3] | S.S. Gubser, I.R. Klebanov and A.W. Peet, Entropy and temperature of black 3-branes, Phys. Rev.D 54 (1996) 3915 [hep-th/9602135] [INSPIRE]. |

[4] | O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE]. · Zbl 1368.81009 |

[5] | D.N. Kabat and G. Lifschytz, Approximations for strongly coupled supersymmetric quantum mechanics, Nucl. Phys.B 571 (2000) 419 [hep-th/9910001] [INSPIRE]. · Zbl 1028.81507 |

[6] | D.N. Kabat, G. Lifschytz and D.A. Lowe, Black hole thermodynamics from calculations in strongly coupled gauge theory, Int. J. Mod. Phys.A 16 (2001) 856 [Phys. Rev. Lett.86 (2001) 1426] [hep-th/0007051] [INSPIRE]. · Zbl 0997.83037 |

[7] | D.N. Kabat, G. Lifschytz and D.A. Lowe, Black hole entropy from nonperturbative gauge theory, Phys. Rev.D 64 (2001) 124015 [hep-th/0105171] [INSPIRE]. |

[8] | Y.-H. Lin, S.-H. Shao, Y. Wang and X. Yin, A low temperature expansion for matrix quantum mechanics, JHEP05 (2015) 136 [arXiv:1304.1593] [INSPIRE]. · Zbl 1388.81902 |

[9] | S. Catterall and T. Wiseman, Towards lattice simulation of the gauge theory duals to black holes and hot strings, JHEP12 (2007) 104 [arXiv:0706.3518] [INSPIRE]. · Zbl 1246.81112 |

[10] | M. Hanada, J. Nishimura and S. Takeuchi, Non-lattice simulation for supersymmetric gauge theories in one dimension, Phys. Rev. Lett.99 (2007) 161602 [arXiv:0706.1647] [INSPIRE]. |

[11] | 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]. |

[12] | 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]. |

[13] | D. Kadoh and S. Kamata, One dimensional supersymmetric Yang-Mills theory with 16 supercharges, PoS(LATTICE 2012)064 [arXiv:1212.4919] [INSPIRE]. |

[14] | M. Hanada, Y. Hyakutake, G. Ishiki and J. Nishimura, Holographic description of quantum black hole on a computer, Science344 (2014) 882 [arXiv:1311.5607] [INSPIRE]. |

[15] | S. Catterall, A. Joseph and T. Wiseman, Thermal phases of D1-branes on a circle from lattice super Yang-Mills, JHEP12 (2010) 022 [arXiv:1008.4964] [INSPIRE]. · Zbl 1294.81176 |

[16] | 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]. |

[17] | 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]. |

[18] | K. Becker, M. Becker, J. Polchinski and A.A. Tseytlin, Higher order graviton scattering in M(atrix) theory, Phys. Rev.D 56 (1997) 3174 [hep-th/9706072] [INSPIRE]. |

[19] | Y. Okawa and T. Yoneya, Multibody interactions of D particles in supergravity and matrix theory, Nucl. Phys.B 538 (1999) 67 [hep-th/9806108] [INSPIRE]. · Zbl 0940.83026 |

[20] | Y. Kazama and T. Muramatsu, On the supersymmetry and gauge structure of matrix theory, Nucl. Phys.B 584 (2000) 171 [hep-th/0003161] [INSPIRE]. · Zbl 0984.81157 |

[21] | I.L. Buchbinder, A.Y. 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]. · Zbl 0988.81073 |

[22] | J.-H. Baek, S. Hyun, W. Jang and S.-H. Yi, Membrane dynamics in three dimensional N = 6 supersymmetric Chern-Simons theory, arXiv:0812.1772 [INSPIRE]. |

[23] | S. Paban, S. Sethi and M. Stern, Constraints from extended supersymmetry in quantum mechanics, Nucl. Phys.B 534 (1998) 137 [hep-th/9805018] [INSPIRE]. · Zbl 1078.81532 |

[24] | S. Paban, S. Sethi and M. Stern, Supersymmetry and higher derivative terms in the effective action of Yang-Mills theories, JHEP06 (1998) 012 [hep-th/9806028] [INSPIRE]. · Zbl 0955.81060 |

[25] | G.T. Horowitz and E.J. Martinec, Comments on black holes in matrix theory, Phys. Rev.D 57 (1998) 4935 [hep-th/9710217] [INSPIRE]. |

[26] | M. Li, Matrix Schwarzschild black holes in large-N limit, JHEP01 (1998) 009 [hep-th/9710226] [INSPIRE]. · Zbl 0958.81064 |

[27] | T. Banks, W. Fischler, I.R. Klebanov and L. Susskind, Schwarzschild black holes in matrix theory. 2, JHEP01 (1998) 008 [hep-th/9711005] [INSPIRE]. · Zbl 0955.83023 |

[28] | M. Li and E.J. Martinec, Probing matrix black holes, hep-th/9801070 [INSPIRE]. · Zbl 0904.53059 |

[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] | D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP04 (2002) 013 [hep-th/0202021] [INSPIRE]. |

[32] | M.S. Costa, L. Greenspan, J. Penedones and J. Santos, Thermodynamics of the BMN matrix model at strong coupling, JHEP03 (2015) 069 [arXiv:1411.5541] [INSPIRE]. · Zbl 1388.83649 |

[33] | T. Morita and S. Shiba, Thermodynamics of black M-branes from SCFTs, JHEP07 (2013) 100 [arXiv:1305.0789] [INSPIRE]. · Zbl 1342.83410 |

[34] | O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10 (2008) 091 [arXiv:0806.1218] [INSPIRE]. · Zbl 1245.81130 |

[35] | 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 |

[36] | T. Morita and S. Shiba, Microstates of D1-D5(-P) black holes as interacting D-branes, Phys. Lett.B 747 (2015) 164 [arXiv:1410.8319] [INSPIRE]. · Zbl 1369.83094 |

[37] | E.J. Martinec and V. Sahakian, Black holes and the super Yang-Mills phase diagram. 2, Phys. Rev.D 59 (1999) 124005 [hep-th/9810224] [INSPIRE]. |

[38] | L. Susskind, Matrix theory black holes and the Gross-Witten transition, hep-th/9805115 [INSPIRE]. · Zbl 1013.83027 |

[39] | J.L.F. Barbon, I.I. Kogan and E. Rabinovici, On stringy thresholds in SYM/AdS thermodynamics, Nucl. Phys.B 544 (1999) 104 [hep-th/9809033] [INSPIRE]. · Zbl 0958.81114 |

[40] | O. Aharony, J. Marsano, S. Minwalla and T. Wiseman, Black hole-black string phase transitions in thermal 1 + 1 dimensional supersymmetric Yang-Mills theory on a circle, Class. Quant. Grav.21 (2004) 5169 [hep-th/0406210] [INSPIRE]. · Zbl 1062.83065 |

[41] | G. Mandal, M. Mahato and T. Morita, Phases of one dimensional large-N gauge theory in a 1/D expansion, JHEP02 (2010) 034 [arXiv:0910.4526] [INSPIRE]. · Zbl 1270.81184 |

[42] | G. Mandal and T. Morita, Phases of a two dimensional large-N gauge theory on a torus, Phys. Rev.D 84 (2011) 085007 [arXiv:1103.1558] [INSPIRE]. |

[43] | A.W. Peet and J. Polchinski, UV/IR relations in AdS dynamics, Phys. Rev.D 59 (1999) 065011 [hep-th/9809022] [INSPIRE]. |

[44] | J. Ambjørn, Y.M. Makeenko and G.W. Semenoff, Thermodynamics of D0-branes in matrix theory, Phys. Lett.B 445 (1999) 307 [hep-th/9810170] [INSPIRE]. · Zbl 1058.81625 |

[45] | T. Hotta, J. Nishimura and A. Tsuchiya, Dynamical aspects of large-N reduced models, Nucl. Phys.B 545 (1999) 543 [hep-th/9811220] [INSPIRE]. |

[46] | J.A. Harvey, G.W. Moore and A. Strominger, Reducing S duality to T duality, Phys. Rev.D 52 (1995) 7161 [hep-th/9501022] [INSPIRE]. |

[47] | M. Bershadsky, A. Johansen, V. Sadov and C. Vafa, Topological reduction of 4D SYM to 2D σ-models, Nucl. Phys.B 448 (1995) 166 [hep-th/9501096] [INSPIRE]. · Zbl 1009.58502 |

[48] | R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Matrix string theory, Nucl. Phys.B 500 (1997) 43 [hep-th/9703030] [INSPIRE]. · Zbl 0934.81044 |

[49] | 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]. |

[50] | I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP09 (2008) 094 [arXiv:0807.3324] [INSPIRE]. · Zbl 1245.81187 |

[51] | G.T. Horowitz and J. Polchinski, A correspondence principle for black holes and strings, Phys. Rev.D 55 (1997) 6189 [hep-th/9612146] [INSPIRE]. |

[52] | 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 (1998) 202 [hep-th/9805156] [INSPIRE]. · Zbl 1078.81563 |

[53] | 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]. |

[54] | M. Hanada, A. Miwa, J. Nishimura and S. Takeuchi, Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics, Phys. Rev. Lett.102 (2009) 181602 [arXiv:0811.2081] [INSPIRE]. |

[55] | G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev.D 59 (1998) 026005 [hep-th/9808079] [INSPIRE]. |

[56] | O. Aharony et al., The phase structure of low dimensional large-N gauge theories on tori, JHEP01 (2006) 140 [hep-th/0508077] [INSPIRE]. |

[57] | G. Mandal and T. Morita, Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD, JHEP09 (2011) 073 [arXiv:1107.4048] [INSPIRE]. · Zbl 1301.81306 |

[58] | R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett.70 (1993) 2837 [hep-th/9301052] [INSPIRE]. · Zbl 1051.83544 |

[59] | G.T. Horowitz and T. Wiseman, General black holes in Kaluza-Klein theory, arXiv:1107.5563 [INSPIRE]. · Zbl 1259.83004 |

[60] | N. Kawahara, J. Nishimura and S. Takeuchi, Phase structure of matrix quantum mechanics at finite temperature, JHEP10 (2007) 097 [arXiv:0706.3517] [INSPIRE]. |

[61] | T. Azuma, T. Morita and S. Takeuchi, Hagedorn instability in dimensionally reduced large-N gauge theories as Gregory-Laflamme and Rayleigh-Plateau instabilities, Phys. Rev. Lett.113 (2014) 091603 [arXiv:1403.7764] [INSPIRE]. |

[62] | W. Taylor, D-brane field theory on compact spaces, Phys. Lett.B 394 (1997) 283 [hep-th/9611042] [INSPIRE]. |

[63] | J. Polchinski and P. Pouliot, Membrane scattering with M momentum transfer, Phys. Rev.D 56 (1997) 6601 [hep-th/9704029] [INSPIRE]. |

[64] | N. Dorey, V.V. Khoze and M.P. Mattis, Multi-instantons, three-dimensional gauge theory and the Gauss-Bonnet-Chern theorem, Nucl. Phys.B 502 (1997) 94 [hep-th/9704197] [INSPIRE]. · Zbl 0935.81073 |

[65] | C. Fraser and D. Tong, Instantons, three-dimensional gauge theories and monopole moduli spaces, Phys. Rev.D 58 (1998) 085001 [hep-th/9710098] [INSPIRE]. |

[66] | E.J. Martinec and V. Sahakian, Black holes and five-brane thermodynamics, Phys. Rev.D 60 (1999) 064002 [hep-th/9901135] [INSPIRE]. |

[67] | E. Eyras, B. Janssen and Y. Lozano, Five-branes, KK monopoles and T duality, Nucl. Phys.B 531 (1998) 275 [hep-th/9806169] [INSPIRE]. · Zbl 0961.81087 |

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