Abstract
We present results of lattice simulations of the Plane Wave Matrix Model (PWMM). The PWMM is a theory of supersymmetric quantum mechanics that has a well-defined canonical ensemble. We simulate this theory by applying rational hybrid Monte Carlo techniques to a naïve lattice action. We examine the strong coupling behaviour of the model focussing on the deconfinement transition.
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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] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
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] [SPIRES].
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] [SPIRES].
S. Catterall and T. Wiseman, Black hole thermodynamics from simulations of lattice Yang-Mills theory, Phys. Rev. D 78 (2008) 041502 [arXiv:0803.4273] [SPIRES].
S. Catterall and T. Wiseman, Extracting black hole physics from the lattice, JHEP 04 (2010) 077 [arXiv:0909.4947] [SPIRES].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [SPIRES].
H. Lin and J.M. Maldacena, Fivebranes from gauge theory, Phys. Rev. D 74 (2006) 084014 [hep-th/0509235] [SPIRES].
G. van Anders, General Lin-Maldacena solutions and PWMM instantons from supergravity, JHEP 03 (2007) 028 [hep-th/0701277] [SPIRES].
H. Ling, A.R. Mohazab, H.-H. Shieh, G. van Anders and M. Van Raamsdonk, Little string theory from a double-scaled matrix model, JHEP 10 (2006) 018 [hep-th/0606014] [SPIRES].
T. Ishii, G. Ishiki, S. Shimasaki and A. Tsuchiya, N = 4 super Yang-Mills from the plane wave matrix model, Phys. Rev. D 78 (2008) 106001 [arXiv:0807.2352] [SPIRES].
S. Catterall, D.B. Kaplan and M. Ünsal, Exact lattice supersymmetry, Phys. Rept. 484 (2009) 71 [arXiv:0903.4881] [SPIRES].
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] [SPIRES].
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] [SPIRES].
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] [SPIRES].
G. Ishiki, Y. Takayama and A. Tsuchiya, N = 4 SYM on R × S 3 and theories with 16 supercharges, JHEP 10 (2006) 007 [hep-th/0605163] [SPIRES].
G. Ishiki, S. Shimasaki, Y. Takayama and A. Tsuchiya, Embedding of theories with SU(2|4) symmetry into the plane wave matrix model, JHEP 11 (2006) 089 [hep-th/0610038] [SPIRES].
G. Ishiki, S.-W. Kim, J. Nishimura and A. Tsuchiya, Deconfinement phase transition in N = 4 super Yang-Mills theory on R × S 3 from supersymmetric matrix quantum mechanics, Phys. Rev. Lett. 102 (2009) 111601 [arXiv:0810.2884] [SPIRES].
G. Ishiki, S.-W. Kim, J. Nishimura and A. Tsuchiya, Testing a novel large-N reduction for N = 4 super Yang-Mills theory on R × S 3, JHEP 09 (2009) 029 [arXiv:0907.1488] [SPIRES].
M.A. Clark, A.D. Kennedy and Z. Sroczynski, Exact 2 + 1 flavour RHMC simulations, Nucl. Phys. Proc. Suppl. 140 (2005) 835 [hep-lat/0409133] [SPIRES].
B. Jegerlehner, Krylov space solvers for shifted linear systems, hep-lat/9612014 [SPIRES].
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A.H. Teller and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21 (1953) 1087.
S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Hybrid Monte Carlo, Phys. Lett. B 195 (1987) 216 [SPIRES].
S.W. Hawking and D.N. Page, Thermodynamics of black holes in Anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [SPIRES].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [SPIRES].
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] [SPIRES].
K. Furuuchi, E. Schreiber and G.W. Semenoff, Five-brane thermodynamics from the matrix model, hep-th/0310286 [SPIRES].
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] [SPIRES].
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] [SPIRES].
N. Kawahara, J. Nishimura and S. Takeuchi, High temperature expansion in supersymmetric matrix quantum mechanics, JHEP 12 (2007) 103 [arXiv:0710.2188] [SPIRES].
J. Nishimura, Non-lattice simulation of supersymmetric gauge theories as a probe to quantum black holes and strings, PoS(LAT2009)016 [arXiv:0912.0327] [SPIRES].
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ArXiv ePrint: 1003.4952
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Catterall, S., van Anders, G. First results from lattice simulation of the PWMM. J. High Energ. Phys. 2010, 88 (2010). https://doi.org/10.1007/JHEP09(2010)088
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DOI: https://doi.org/10.1007/JHEP09(2010)088