Abstract
We study the bosonic part of the BMN matrix model for wide ranges of temperatures, values of the deformation parameter, and numbers of colors 16 ≤ N ≤ 48. Using lattice computations, we analyze phase transitions in the model, observing a single first-order transition from a uniform to a gapped phase for all values of the deformation parameter. We study the functional form of the dependence of the critical temperature on the deformation parameter, to describe how our results smoothly interpolate between the limits of the bosonic BFSS model and the gauged Gaussian model.
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I.R. Klebanov, String theory in two-dimensions, in Spring School on String Theory and Quantum Gravity (to be followed by Workshop), (1991) [hep-th/9108019] [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].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
D.N. Kabat and G. Lifschytz, Approximations for strongly coupled supersymmetric quantum mechanics, Nucl. Phys. B 571 (2000) 419 [hep-th/9910001] [INSPIRE].
T. Wiseman, On black hole thermodynamics from super Yang-Mills, JHEP 07 (2013) 101 [arXiv:1304.3938] [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].
S. Catterall and G. van Anders, First Results from Lattice Simulation of the PWMM, JHEP 09 (2010) 088 [arXiv:1003.4952] [INSPIRE].
D. Kadoh and S. Kamata, Gauge/gravity duality and lattice simulations of one dimensional SYM with sixteen supercharges, arXiv:1503.08499 [INSPIRE].
V.G. Filev and D. O’Connor, The BFSS model on the lattice, JHEP 05 (2016) 167 [arXiv:1506.01366] [INSPIRE].
E. Berkowitz, E. Rinaldi, M. Hanada, G. Ishiki, S. Shimasaki and P. Vranas, Supergravity from D0-brane Quantum Mechanics, arXiv:1606.04948 [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].
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].
R.G. Jha, S. Catterall, D. Schaich and T. Wiseman, Testing the holographic principle using lattice simulations, EPJ Web Conf. 175 (2018) 08004 [arXiv:1710.06398] [INSPIRE].
Y. Asano, V.G. Filev, S. Kováčik and D. O’Connor, The non-perturbative phase diagram of the BMN matrix model, JHEP 07 (2018) 152 [arXiv:1805.05314] [INSPIRE].
D. Schaich, Progress and prospects of lattice supersymmetry, PoS LATTICE2018 (2019) 005 [arXiv:1810.09282] [INSPIRE].
S. Catterall, J. Giedt, R.G. Jha, D. Schaich and T. Wiseman, Three-dimensional super-Yang-Mills theory on the lattice and dual black branes, Phys. Rev. D 102 (2020) 106009 [arXiv:2010.00026] [INSPIRE].
MCSMC collaboration, Confinement/deconfinement transition in the D0-brane matrix model — A signature of M-theory?, JHEP 05 (2022) 096 [arXiv:2110.01312] [INSPIRE].
D. Schaich, R.G. Jha and A. Joseph, Thermal phase structure of dimensionally reduced super-Yang-Mills, PoS LATTICE2021 (2022) 187 [arXiv:2201.03097] [INSPIRE].
A. Sherletov and D. Schaich, Investigations of supersymmetric Yang-Mills theories, PoS LATTICE2021 (2022) 031 [arXiv:2201.08626] [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].
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].
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, J. Nishimura, Y. Sekino and T. Yoneya, Monte Carlo studies of Matrix theory correlation functions, Phys. Rev. Lett. 104 (2010) 151601 [arXiv:0911.1623] [INSPIRE].
M. Hanada, J. Nishimura, Y. Sekino and T. Yoneya, Direct test of the gauge-gravity correspondence for Matrix theory correlation functions, JHEP 12 (2011) 020 [arXiv:1108.5153] [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].
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].
M.S. Costa, L. Greenspan, J. Penedones and J. Santos, Thermodynamics of the BMN matrix model at strong coupling, JHEP 03 (2015) 069 [arXiv:1411.5541] [INSPIRE].
S. Kováčik, D. O’Connor and Y. Asano, The nonperturbative phase diagram of the bosonic BMN matrix model, PoS CORFU2019 (2020) 221 [arXiv:2004.05820] [INSPIRE].
Y. Asano, S. Kováčik and D. O’Connor, The Confining Transition in the Bosonic BMN Matrix Model, JHEP 06 (2020) 174 [arXiv:2001.03749] [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].
G. Bergner, N. Bodendorfer, M. Hanada, E. Rinaldi, A. Schäfer and P. Vranas, Thermal phase transition in Yang-Mills matrix model, JHEP 01 (2020) 053 [arXiv:1909.04592] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn/deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
K. Furuuchi, E. Schreiber and G.W. Semenoff, Five-brane thermodynamics from the matrix model, hep-th/0310286 [INSPIRE].
N.S. Dhindsa, R.G. Jha, A. Joseph, A. Samlodia and D. Schaich, Non-perturbative phase structure of the bosonic BMN matrix model — data release, https://doi.org/10.5281/zenodo.6462432 (2022).
K. Dasgupta, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Matrix perturbation theory for M-theory on a PP wave, JHEP 05 (2002) 056 [hep-th/0205185] [INSPIRE].
K. Dasgupta, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Protected multiplets of M-theory on a plane wave, JHEP 09 (2002) 021 [hep-th/0207050] [INSPIRE].
D. Schaich and T. DeGrand, Parallel software for lattice N = 4 supersymmetric Yang-Mills theory, Comput. Phys. Commun. 190 (2015) 200 [arXiv:1410.6971] [INSPIRE].
A. Francis, O. Kaczmarek, M. Laine, T. Neuhaus and H. Ohno, Critical point and scale setting in SU(3) plasma: An update, Phys. Rev. D 91 (2015) 096002 [arXiv:1503.05652] [INSPIRE].
M. Spradlin, M. Van Raamsdonk and A. Volovich, Two-loop partition function in the planar plane-wave matrix model, Phys. Lett. B 603 (2004) 239 [hep-th/0409178] [INSPIRE].
S. Hadizadeh, B. Ramadanovic, G.W. Semenoff and D. Young, Free energy and phase transition of the matrix model on a plane-wave, Phys. Rev. D 71 (2005) 065016 [hep-th/0409318] [INSPIRE].
M. Fukugita, H. Mino, M. Okawa and A. Ukawa, Finite Size Test for the Finite Temperature Chiral Phase Transition in Lattice QCD, Phys. Rev. Lett. 65 (1990) 816 [INSPIRE].
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].
T. Morita and H. Yoshida, Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models, Phys. Rev. D 101 (2020) 106010 [arXiv:2001.02109] [INSPIRE].
J. Maldacena and A. Milekhin, To gauge or not to gauge?, JHEP 04 (2018) 084 [arXiv:1802.00428] [INSPIRE].
E. Berkowitz, M. Hanada, E. Rinaldi and P. Vranas, Gauged And Ungauged: A Nonperturbative Test, JHEP 06 (2018) 124 [arXiv:1802.02985] [INSPIRE].
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Dhindsa, N.S., Jha, R.G., Joseph, A. et al. Non-perturbative phase structure of the bosonic BMN matrix model. J. High Energ. Phys. 2022, 169 (2022). https://doi.org/10.1007/JHEP05(2022)169
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DOI: https://doi.org/10.1007/JHEP05(2022)169