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Gauged and ungauged: a nonperturbative test

A preprint version of the article is available at arXiv.

Abstract

We study the thermodynamics of the ‘ungauged’ D0-brane matrix model by Monte Carlo simulation. Our results appear to be consistent with the conjecture by Maldacena and Milekhin.

References

  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] [INSPIRE].

  2. J.B. Kogut and L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D 11 (1975) 395 [INSPIRE].

    ADS  Google Scholar 

  3. E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. S. Ghosh, R.M. Soni and S.P. Trivedi, On the entanglement entropy for gauge theories, JHEP 09 (2015) 069 [arXiv:1501.02593] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  5. S. Aoki et al., On the definition of entanglement entropy in lattice gauge theories, JHEP 06 (2015) 187 [arXiv:1502.04267] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  6. M. Hanada, J. Maltz and L. Susskind, Deconfinement transition as black hole formation by the condensation of QCD strings, Phys. Rev. D 90 (2014) 105019 [arXiv:1405.1732] [INSPIRE].

    ADS  Google Scholar 

  7. J. Maldacena and A. Milekhin, To gauge or not to gauge?, JHEP 04 (2018) 084 [arXiv:1802.00428] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  8. 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].

    ADS  MathSciNet  MATH  Google Scholar 

  9. B. de Wit, J. Hoppe and H. Nicolai, On the quantum mechanics of supermembranes, Nucl. Phys. B 305 (1988) 545 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  10. 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].

    ADS  MathSciNet  Google Scholar 

  11. E. Berkowitz et al., Precision lattice test of the gauge/gravity duality at large-N , Phys. Rev. D 94 (2016) 094501 [arXiv:1606.04951] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  12. 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].

    ADS  Article  Google Scholar 

  13. 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].

    ADS  MathSciNet  Google Scholar 

  14. 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].

    ADS  Article  Google Scholar 

  15. D. Kadoh and S. Kamata, One dimensional supersymmetric Yang-Mills theory with 16 supercharges, PoS(LATTICE 2012)064 [arXiv:1212.4919] [INSPIRE].

  16. 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].

    ADS  Article  Google Scholar 

  17. D. Kadoh and S. Kamata, Gauge/gravity duality and lattice simulations of one dimensional SYM with sixteen supercharges, arXiv:1503.08499 [INSPIRE].

  18. V.G. Filev and D. O’Connor, A computer test of holographic flavour dynamics, JHEP 05 (2016) 122 [arXiv:1512.02536] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  19. 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].

    ADS  MathSciNet  Google Scholar 

  20. 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].

    ADS  Article  Google Scholar 

  21. J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  22. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  23. Y. Sekino and T. Yoneya, Generalized AdS/CFT correspondence for matrix theory in the large N limit, Nucl. Phys. B 570 (2000) 174 [hep-th/9907029] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  24. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  25. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  26. L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE].

  27. E. Halyo, A. Rajaraman and L. Susskind, Braneless black holes, Phys. Lett. B 392 (1997) 319 [hep-th/9605112] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  28. G.T. Horowitz and J. Polchinski, A Correspondence principle for black holes and strings, Phys. Rev. D 55 (1997) 6189 [hep-th/9612146] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  29. M. Hanada, MMMM, https://sites.google.com/site/hanadamasanori/home/mmmm.

  30. 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] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  31. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  32. O. Aharony et al., The Phase structure of low dimensional large N gauge theories on Tori, JHEP 01 (2006) 140 [hep-th/0508077] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  33. N. Kawahara, J. Nishimura and S. Takeuchi, Phase structure of matrix quantum mechanics at finite temperature, JHEP 10 (2007) 097 [arXiv:0706.3517] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  34. 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].

    ADS  Article  MATH  Google Scholar 

  35. T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large N gauge theory, Phys. Rev. Lett. 48 (1982) 1063 [INSPIRE].

    ADS  Article  Google Scholar 

  36. B. de Wit, M. Lüscher and H. Nicolai, The supermembrane is unstable, Nucl. Phys. B 320 (1989) 135 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  37. A.V. Smilga, Super-Yang-Mills quantum mechanics and supermembrane spectrum, in the proceedings of the Trieste Conference on Supermembranes and Physics in 2 + 1 Dimensions, July 17-21, Trieste Italy (1989), arXiv:1406.5987 [INSPIRE].

  38. E. Berkowitz, M. Hanada and J. Maltz, Chaos in matrix models and black hole evaporation, Phys. Rev. D 94 (2016) 126009 [arXiv:1602.01473] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  39. V. Pestun et al., Localization techniques in quantum field theories, J. Phys. A 50 (2017) 440301 [arXiv:1608.02952] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  40. U.H. Danielsson, G. Ferretti and B. Sundborg, D particle dynamics and bound states, Int. J. Mod. Phys. A 11 (1996) 5463 [hep-th/9603081] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  41. D.N. Kabat and P. Pouliot, A Comment on zero-brane quantum mechanics, Phys. Rev. Lett. 77 (1996) 1004 [hep-th/9603127] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  42. K. Becker, M. Becker, J. Polchinski and A.A. Tseytlin, Higher order graviton scattering in M(atrix) theory, Phys. Rev. D 56 (1997) R3174 [hep-th/9706072] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

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Correspondence to Enrico Rinaldi.

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ArXiv ePrint: 1802.02985

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Berkowitz, E., Hanada, M., Rinaldi, E. et al. Gauged and ungauged: a nonperturbative test. J. High Energ. Phys. 2018, 124 (2018). https://doi.org/10.1007/JHEP06(2018)124

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  • DOI: https://doi.org/10.1007/JHEP06(2018)124

Keywords

  • Gauge-gravity correspondence
  • Lattice Quantum Field Theory
  • M(atrix) Theories