Abstract
In this paper, we study the finite-temperature matrix quantum mechanics with chemical potential term linear in the single trace of U(N) matrices, via Monte Carlo simulation. In the bosonic case, we exhibit the existence of the Gross-Witten-Wadia (GWW) type third-order phase transition. We also extend our studies to the model with the fermionic degrees of freedom employing the non-lattice simulation via Fourier expansion, and explore the possibilities that there is a phase transition between the gapped and ungapped phase both in the absence and presence of the chemical potential term. We make a comparison of the phase diagram between the bosonic and fermionic cases.
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References
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].
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].
L. Álvarez-Gaumé, C. Gomez, H. Liu and S. Wadia, Finite temperature effective action, AdS 5 black holes and 1/N expansion, Phys. Rev. D 71 (2005) 124023 [hep-th/0502227] [INSPIRE].
L. Álvarez-Gaumé, P. Basu, M. Mariño and S.R. Wadia, Blackhole/string transition for the small Schwarzschild blackhole of AdS 5 × S 5 and critical unitary matrix models, Eur. Phys. J. C 48 (2006) 647 [hep-th/0605041] [INSPIRE].
T. Azuma, P. Basu and S.R. Wadia, Monte Carlo studies of the GWW phase transition in large-N gauge theories, Phys. Lett. B 659 (2008) 676 [arXiv:0710.5873] [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. Wadia, A study of U(N) lattice gauge theory in two-dimensions, EFI-79/44-CHICAGO.
S.R. Wadia, N = ∞ phase transition in a class of exactly soluble model lattice gauge theories, Phys. Lett. 93B (1980) 403 [INSPIRE].
M. Headrick, Hedgehog black holes and the Polyakov loop at strong coupling, Phys. Rev. D 77 (2008) 105017 [arXiv:0712.4155] [INSPIRE].
O. Aharony et al., The phase structure of low dimensional large-N gauge theories on Tori, JHEP 01 (2006) 140 [hep-th/0508077] [INSPIRE].
N. Kawahara, J. Nishimura and S. Takeuchi, Exact fuzzy sphere thermodynamics in matrix quantum mechanics, JHEP 05 (2007) 091 [arXiv:0704.3183] [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].
N. Kawahara, J. Nishimura and S. Takeuchi, High temperature expansion in supersymmetric matrix quantum mechanics, JHEP 12 (2007) 103 [arXiv:0710.2188] [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].
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].
T. Azuma, T. Morita and S. Takeuchi, New states of gauge theories on a circle, JHEP 10 (2012) 059 [arXiv:1207.3323] [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].
K. Furuuchi, E. Schreiber and G.W. Semenoff, Five-brane thermodynamics from the matrix model, hep-th/0310286 [INSPIRE].
N. Kawahara, J. Nishimura and K. Yoshida, Dynamical aspects of the plane-wave matrix model at finite temperature, JHEP 06 (2006) 052 [hep-th/0601170] [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].
P. Basu and S.R. Wadia, R-charged AdS 5 black holes and large-N unitary matrix models, Phys. Rev. D 73 (2006) 045022 [hep-th/0506203] [INSPIRE].
P. Basu and A. Mukherjee, Dissolved deconfinement: phase structure of large-N gauge theories with fundamental matter, Phys. Rev. D 78 (2008) 045012 [arXiv:0803.1880] [INSPIRE].
S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Hybrid Monte Carlo, Phys. Lett. B 195 (1987) 216 [INSPIRE].
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].
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].
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. Hanada, S. Matsuura, J. Nishimura and D. Robles-Llana, Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature, JHEP 02 (2011) 060 [arXiv:1012.2913] [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].
A.D. Kennedy, I. Horvath and S. Sint, A new exact method for dynamical fermion computations with nonlocal actions, Nucl. Phys. Proc. Suppl. 73 (1999) 834 [hep-lat/9809092] [INSPIRE].
B. Jegerlehner, Krylov space solvers for shifted linear systems, hep-lat/9612014 [INSPIRE].
B. Ydri, Computational physics: an introduction to Monte Carlo simulations of matrix field theory, arXiv:1506.02567.
T.J. Hollowood, S.P. Kumar and J.C. Myers, Weak coupling large-N transitions at finite baryon density, JHEP 11 (2011) 138 [arXiv:1110.0696] [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
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ArXiv ePrint: 1707.02898
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Azuma, T., Basu, P. & Samantray, P. Phase transitions of a (super) quantum mechanical matrix model with a chemical potential. J. High Energ. Phys. 2017, 71 (2017). https://doi.org/10.1007/JHEP09(2017)071
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DOI: https://doi.org/10.1007/JHEP09(2017)071