Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature
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Abstract
We investigate thermodynamic properties of one-dimensional U(N) supersymmetric gauge theories with 4 and 8 supercharges in the planar large-N limit by Monte Carlo calculations. Unlike the 16 supercharge case, the threshold bound state with zero energy is widely believed not to exist in these models. This led A.V.Smilga to conjecture that the internal energy decreases exponentially at low temperature instead of decreasing with a power law. In the 16 supercharge case, the latter behavior was predicted from the dual black 0-brane geometry and confirmed recently by Monte Carlo calculations. Our results for the models with 4 and 8 supercharges indeed support the exponential behavior, revealing a qualitative difference from the 16 supercharge case.
Keywords
Supersymmetric gauge theory Field Theories in Lower Dimensions Nonperturbative EffectsReferences
- [1]J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].MathSciNetMATHCrossRefGoogle Scholar
- [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] [SPIRES].MathSciNetADSGoogle Scholar
- [3]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].ADSCrossRefGoogle Scholar
- [4]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].ADSCrossRefGoogle Scholar
- [5]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] [SPIRES].ADSCrossRefGoogle Scholar
- [6]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] [SPIRES].ADSCrossRefGoogle Scholar
- [7]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] [SPIRES].ADSCrossRefGoogle Scholar
- [8]S. Catterall and T. Wiseman, Towards lattice simulation of the gauge theory duals to black holes and hot strings, JHEP 12 (2007) 104 [arXiv:0706.3518] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
- [9]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].MathSciNetADSGoogle Scholar
- [10]S. Catterall and T. Wiseman, Extracting black hole physics from the lattice, JHEP 04 (2010) 077 [arXiv:0909.4947] [SPIRES].ADSCrossRefGoogle Scholar
- [11]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] [SPIRES].MathSciNetADSGoogle Scholar
- [12]D.N. Kabat, G. Lifschytz and D.A. Lowe, Black hole entropy from non-perturbative gauge theory, Phys. Rev. D 64 (2001) 124015 [hep-th/0105171] [SPIRES].MathSciNetADSGoogle Scholar
- [13]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].MathSciNetADSGoogle Scholar
- [14]A.V. Smilga, Witten index calculation in supersymmetric gauge theory, Nucl. Phys. B 266 (1986) 45 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
- [15]B. de Wit, M. Luscher and H. Nicolai, The supermembrane is unstable, Nucl. Phys. B 320 (1989) 135 [SPIRES].ADSCrossRefGoogle Scholar
- [16]A.V. Smilga, Super Yang-Mills quantum mechanics and supermembrane spectrum, in Proceedings of the Workshop on Supermembranes and (2+ 1)-Dimensional Physics, Trieste Italy, July 16–23 1989, World Scientific (1990), pg. 182.Google Scholar
- [17]P. Yi, Witten index and threshold bound states of D-branes, Nucl. Phys. B 505 (1997) 307 [hep-th/9704098] [SPIRES].ADSCrossRefGoogle Scholar
- [18]S. Sethi and M. Stern, D-brane bound states redux, Commun. Math. Phys. 194 (1998) 675 [hep-th/9705046] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
- [19]G.W. Moore, N. Nekrasov and S. Shatashvili, D-particle bound states and generalized instantons, Commun. Math. Phys. 209 (2000) 77 [hep-th/9803265] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
- [20]A.V. Smilga, Comments on thermodynamics of supersymmetric matrix models, Nucl. Phys. B 818 (2009) 101 [arXiv:0812.4753] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
- [21]M. Campostrini and J. Wosiek, High precision study of the structure of D = 4 supersymmetric Yang-Mills quantum mechanics, Nucl. Phys. B 703 (2004) 454 [hep-th/0407021] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
- [22]J. Ambjørn, K.N. Anagnostopoulos, W. Bietenholz, T. Hotta and J. Nishimura, Large-N dynamics of dimensionally reduced 4D SU(N) super Yang-Mills theory, JHEP 07 (2000) 013 [hep-th/0003208] [SPIRES].ADSCrossRefGoogle Scholar
- [23]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].ADSCrossRefGoogle Scholar
- [24]N. Kawahara, J. Nishimura and S. Takeuchi, High temperature expansion in supersymmetric matrix quantum mechanics, JHEP 12 (2007) 103 [arXiv:0710.2188] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
- [25]W. Krauth and M. Staudacher, Eigenvalue distributions in Yang-Mills integrals, Phys. Lett. B 453 (1999) 253 [hep-th/9902113] [SPIRES].MathSciNetADSGoogle Scholar
- [26]R.A. Janik and J. Wosiek, Towards the matrix model of M-theory on a lattice, Acta Phys. Polon. B 32 (2001) 2143 [hep-th/0003121] [SPIRES].ADSGoogle Scholar
- [27]P. Bialas and J. Wosiek, Towards the lattice study of M-theory (II), Nucl. Phys. Proc. Suppl. 106 (2002) 968 [hep-lat/0111034] [SPIRES].ADSCrossRefGoogle Scholar
- [28]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] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
- [29]N. Kawahara, J. Nishimura and S. Takeuchi, Phase structure of matrix quantum mechanics at finite temperature, JHEP 10 (2007) 097 [arXiv:0706.3517] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
- [30]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] [SPIRES].ADSCrossRefGoogle Scholar
- [31]T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large-N gauge theory, Phys. Rev. Lett. 48 (1982) 1063 [SPIRES].ADSCrossRefGoogle Scholar
- [32]R. Narayanan and H. Neuberger, Large-N reduction in continuum, Phys. Rev. Lett. 91 (2003) 081601 [hep-lat/0303023] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
- [33]K. Furuuchi, E. Schreiber and G.W. Semenoff, Five-brane thermodynamics from the matrix model, hep-th/0310286 [SPIRES].
- [34]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].MathSciNetMATHGoogle Scholar
- [35]K. Becker and M. Becker, A two-loop test of M(atrix) theory, Nucl. Phys. B 506 (1997) 48 [hep-th/9705091] [SPIRES].ADSCrossRefGoogle Scholar
- [36]Y. Okawa and T. Yoneya, Multi-body interactions of D-particles in supergravity and Matrix theory, Nucl. Phys. B 538 (1999) 67 [hep-th/9806108] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
- [37]A.V. Smilga, Born-Oppenheimer corrections to the effective zero-mode Hamiltonian in SYM theory, JHEP 04 (2002) 054 [hep-th/0201048] [SPIRES].MathSciNetADSCrossRefGoogle Scholar