Abstract
We perform microcanonical classical statistical lattice simulations of SU(N) Yang-Mills theory with eight scalars on a circle. Measuring the eigenvalue distribution of the spatial Wilson loop we find two distinct phases depending on the total energy and circle radius, which we tentatively interpret as corresponding to black hole and black string phases in a dual gravity picture. We proceed to study quenches by first preparing the system in one phase, rapidly changing the total energy, and monitoring the real-time system response. We observe that the system relaxes to the equilibrium phase corresponding to the new energy, in the process exhibiting characteristic damped oscillations. We interpret this as the topology change from black hole to black string configurations, with damped oscillations corresponding to quasi-normal mode ringing of the black hole/black string final state. This would suggest that α′ corrections alone can resolve the singularity associated with the topology change. We extract the real and imaginary part of the lowest-lying presumptive quasinormal mode as a function of energy and N.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
M.W. Choptuik, L. Lehner, I. Olabarrieta, R. Petryk, F. Pretorius and H. Villegas, Towards the final fate of an unstable black string, Phys. Rev. D 68 (2003) 044001 [gr-qc/0304085] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
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].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas, M. Van Raamsdonk and T. Wiseman, The Phase structure of low dimensional large N gauge theories on Tori, JHEP 01 (2006) 140 [hep-th/0508077] [INSPIRE].
L. Susskind, Matrix theory black holes and the Gross-Witten transition, hep-th/9805115 [INSPIRE].
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].
M. Li, E.J. Martinec and V. Sahakian, Black holes and the SYM phase diagram, Phys. Rev. D 59 (1999) 044035 [hep-th/9809061] [INSPIRE].
E.J. Martinec and V. Sahakian, Black holes and the superYang-Mills phase diagram. 2., Phys. Rev. D 59 (1999) 124005 [hep-th/9810224] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Localised and nonuniform thermal states of super-Yang-Mills on a circle, JHEP 06 (2017) 029 [arXiv:1702.07718] [INSPIRE].
M. Hanada and P. Romatschke, Lattice Simulations of 10d Yang-Mills toroidally compactified to 1d, 2d and 4d, Phys. Rev. D 96 (2017) 094502 [arXiv:1612.06395] [INSPIRE].
D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a spatial lattice, JHEP 05 (2003) 037 [hep-lat/0206019] [INSPIRE].
A.G. Cohen, D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a Euclidean space-time lattice. 1. A Target theory with four supercharges, JHEP 08 (2003) 024 [hep-lat/0302017] [INSPIRE].
A.G. Cohen, D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a Euclidean space-time lattice. 2. Target theories with eight supercharges, JHEP 12 (2003) 031 [hep-lat/0307012] [INSPIRE].
D.B. Kaplan and M. Ünsal, A Euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges, JHEP 09 (2005) 042 [hep-lat/0503039] [INSPIRE].
F. Sugino, A Lattice formulation of superYang-Mills theories with exact supersymmetry, JHEP 01 (2004) 015 [hep-lat/0311021] [INSPIRE].
F. Sugino, SuperYang-Mills theories on the two-dimensional lattice with exact supersymmetry, JHEP 03 (2004) 067 [hep-lat/0401017] [INSPIRE].
F. Sugino, Various super Yang-Mills theories with exact supersymmetry on the lattice, JHEP 01 (2005) 016 [hep-lat/0410035] [INSPIRE].
S. Catterall, A Geometrical approach to N = 2 super Yang-Mills theory on the two dimensional lattice, JHEP 11 (2004) 006 [hep-lat/0410052] [INSPIRE].
S. Catterall, Lattice formulation of N = 4 super Yang-Mills theory, JHEP 06 (2005) 027 [hep-lat/0503036] [INSPIRE].
A. D’Adda, I. Kanamori, N. Kawamoto and K. Nagata, Exact extended supersymmetry on a lattice: Twisted N = 2 super Yang-Mills in two dimensions, Phys. Lett. B 633 (2006) 645 [hep-lat/0507029] [INSPIRE].
H. Suzuki and Y. Taniguchi, Two-dimensional N = (2, 2) super Yang-Mills theory on the lattice via dimensional reduction, JHEP 10 (2005) 082 [hep-lat/0507019] [INSPIRE].
M. Hanada, D. Kadoh, S. Matsuura and F. Sugino, O(a) Improvement of 2D N = (2, 2) Lattice SYM Theory, Nucl. Phys. B 929 (2018) 266 [arXiv:1711.02319] [INSPIRE].
M. Hanada and I. Kanamori, Lattice study of two-dimensional N = (2, 2) super Yang-Mills at large-N , Phys. Rev. D 80 (2009) 065014 [arXiv:0907.4966] [INSPIRE].
M. Hanada and I. Kanamori, Absence of sign problem in two-dimensional N = (2, 2) super Yang-Mills on lattice, JHEP 01 (2011) 058 [arXiv:1010.2948] [INSPIRE].
E. Giguère and D. Kadoh, Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice, JHEP 05 (2015) 082 [arXiv:1503.04416] [INSPIRE].
D. August, B.H. Wellegehausen and A. Wipf, Mass spectrum of 2-dimensional \( \mathcal{N}=\left(2,2\right) \) super Yang-Mills theory on the lattice, JHEP 01 (2019) 099 [arXiv:1802.07797] [INSPIRE].
S. Catterall, R.G. Jha, D. Schaich and T. Wiseman, Testing holography using lattice super-Yang-Mills theory on a 2-torus, Phys. Rev. D 97 (2018) 086020 [arXiv:1709.07025] [INSPIRE].
S. Catterall, A. Joseph and T. Wiseman, Thermal phases of D1-branes on a circle from lattice super Yang-Mills, JHEP 12 (2010) 022 [arXiv:1008.4964] [INSPIRE].
D. Kadoh, Precision test of the gauge/gravity duality in two-dimensional N = (8, 8) SYM, PoS(LATTICE2016)033 (2017) [arXiv:1702.01615] [INSPIRE].
N. Kawahara, J. Nishimura and S. Takeuchi, Phase structure of matrix quantum mechanics at finite temperature, JHEP 10 (2007) 097 [arXiv:0706.3517] [INSPIRE].
G. Mandal, M. Mahato and T. Morita, Phases of one dimensional large N gauge theory in a 1/D expansion, JHEP 02 (2010) 034 [arXiv:0910.4526] [INSPIRE].
A. Krasnitz and R. Venugopalan, The Initial energy density of gluons produced in very high-energy nuclear collisions, Phys. Rev. Lett. 84 (2000) 4309 [hep-ph/9909203] [INSPIRE].
T. Lappi, Production of gluons in the classical field model for heavy ion collisions, Phys. Rev. C 67 (2003) 054903 [hep-ph/0303076] [INSPIRE].
P. Romatschke and R. Venugopalan, Collective non-Abelian instabilities in a melting color glass condensate, Phys. Rev. Lett. 96 (2006) 062302 [hep-ph/0510121] [INSPIRE].
J. Berges, D. Gelfand, S. Scheffler and D. Sexty, Simulating plasma instabilities in SU(3) gauge theory, Phys. Lett. B 677 (2009) 210 [arXiv:0812.3859] [INSPIRE].
D. Gelfand, A. Ipp and D. Müller, Simulating collisions of thick nuclei in the color glass condensate framework, Phys. Rev. D 94 (2016) 014020 [arXiv:1605.07184] [INSPIRE].
J. Ambjørn, T. Askgaard, H. Porter and M.E. Shaposhnikov, Sphaleron transitions and baryon asymmetry: A Numerical real time analysis, Nucl. Phys. B 353 (1991) 346 [INSPIRE].
D. Bödeker, G.D. Moore and K. Rummukainen, Chern-Simons number diffusion and hard thermal loops on the lattice, Phys. Rev. D 61 (2000) 056003 [hep-ph/9907545] [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].
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].
S. Aoki, M. Hanada and N. Iizuka, Quantum Black Hole Formation in the BFSS Matrix Model, JHEP 07 (2015) 029 [arXiv:1503.05562] [INSPIRE].
T. Kunihiro, B. Müller, A. Ohnishi, A. Schafer, T.T. Takahashi and A. Yamamoto, Chaotic behavior in classical Yang-Mills dynamics, Phys. Rev. D 82 (2010) 114015 [arXiv:1008.1156] [INSPIRE].
G. Gur-Ari, M. Hanada and S.H. Shenker, Chaos in Classical D0-Brane Mechanics, JHEP 02 (2016) 091 [arXiv:1512.00019] [INSPIRE].
A. Rebhan, P. Romatschke and M. Strickland, Hard-loop dynamics of non-Abelian plasma instabilities, Phys. Rev. Lett. 94 (2005) 102303 [hep-ph/0412016] [INSPIRE].
A. Dumitru and Y. Nara, QCD plasma instabilities and isotropization, Phys. Lett. B 621 (2005) 89 [hep-ph/0503121] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, The Fate of non-Abelian plasma instabilities in 3+1 dimensions, Phys. Rev. D 72 (2005) 054003 [hep-ph/0505212] [INSPIRE].
P. Buividovich, M. Hanada and A. Schäfer, Real-time dynamics of matrix quantum mechanics beyond the classical approximation, EPJ Web Conf. 175 (2018) 08006 [arXiv:1711.05556] [INSPIRE].
M. Hanada and T. Nishioka, Cascade of Gregory-Laflamme Transitions and U(1) Breakdown in Super Yang-Mills, JHEP 09 (2007) 012 [arXiv:0706.0188] [INSPIRE].
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].
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].
P. Romatschke, askja: an HMC SU(N ) Code Package in Arbitrary Dimensions, version 1.0 (2016) [https://github.com/paro8929/askja.git].
P. Romatschke and R. Venugopalan, The Unstable Glasma, Phys. Rev. D 74 (2006) 045011 [hep-ph/0605045] [INSPIRE].
H. Kudoh and T. Wiseman, Connecting black holes and black strings, Phys. Rev. Lett. 94 (2005) 161102 [hep-th/0409111] [INSPIRE].
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].
D.J. Gross and E. Witten, Possible Third Order Phase Transition in the Large N Lattice Gauge Theory, Phys. Rev. D 21 (1980) 446 [INSPIRE].
S.R. Wadia, N = ∞ Phase Transition in a Class of Exactly Soluble Model Lattice Gauge Theories, Phys. Lett. B 93 (1980) 403 [INSPIRE].
K. Boguslavski, A. Kurkela, T. Lappi and J. Peuron, Spectral function for overoccupied gluodynamics from real-time lattice simulations, Phys. Rev. D 98 (2018) 014006 [arXiv:1804.01966] [INSPIRE].
F. Aprile and F. Sanfilippo, Quasi-Normal Modes from Non-Commutative Matrix Dynamics, JHEP 09 (2017) 048 [arXiv:1611.00786] [INSPIRE].
N. Iizuka, D.N. Kabat, G. Lifschytz and D.A. Lowe, Stretched horizons, quasiparticles and quasinormal modes, Phys. Rev. D 68 (2003) 084021 [hep-th/0306209] [INSPIRE].
M. Hanada, H. Shimada and M. Tezuka, Universality in Chaos: Lyapunov Spectrum and Random Matrix Theory, Phys. Rev. E 97 (2018) 022224 [arXiv:1702.06935] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Lattice Black Branes: Sphere Packing in General Relativity, JHEP 05 (2018) 111 [arXiv:1712.07663] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1808.08959
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Hanada, M., Romatschke, P. Real time quantum gravity dynamics from classical statistical Yang-Mills simulations. J. High Energ. Phys. 2019, 201 (2019). https://doi.org/10.1007/JHEP01(2019)201
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)201