Skip to main content
Log in

Fast scramblers and non-commutative gauge theories

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

Fast scramblers are quantum systems which thermalize in a time scale logarithmic in the number of degrees of freedom of the system. Non-locality has been argued to be an essential feature of fast scramblers. We provide evidence in support of the crucial role of non-locality in such systems by considering the approach to thermalization in a (strongly-coupled) high temperature non-commutative gauge theory. We show that non-locality inherent to non-commutative gauge theories does indeed accelerate the rate of dissipation in the heat bath in stark contrast to the slow random walk diffusive behavior prevalent in local field theories.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K.S. Thorne, R.H. Price and D.A. Macdonald, Black holes: the membrane paradigm, Yale University Press, Yale U.S.A. (1986).

    Google Scholar 

  2. L. Susskind and J. Lindesay, An introduction to black holes, information and the string theory revolution: the holographic universe, World Scientific, Singapore (2005).

    MATH  Google Scholar 

  3. P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].

    Article  ADS  Google Scholar 

  5. L. Susskind, Addendum to fast scramblers, arXiv:1101.6048 [INSPIRE].

  6. C. Asplund, D. Berenstein and D. Trancanelli, Evidence for fast thermalization in the plane-wave matrix model, Phys. Rev. Lett. 107 (2011) 171602 [arXiv:1104.5469] [INSPIRE].

    Article  ADS  Google Scholar 

  7. J.L. Barbon and J.M. Magan, Chaotic fast scrambling at black holes, Phys. Rev. D 84 (2011) 106012 [arXiv:1105.2581] [INSPIRE].

    ADS  Google Scholar 

  8. N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, Towards the fast scrambling conjecture, arXiv:1111.6580 [INSPIRE].

  9. D. Bigatti and L. Susskind, Magnetic fields, branes and noncommutative geometry, Phys. Rev. D 62 (2000) 066004 [hep-th/9908056] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  10. M.R. Douglas and C.M. Hull, D-branes and the noncommutative torus, JHEP 02 (1998) 008 [hep-th/9711165] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. F. Ardalan, H. Arfaei and M. Sheikh-Jabbari, Noncommutative geometry from strings and branes, JHEP 02 (1999) 016 [hep-th/9810072] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  14. A. Hashimoto and N. Itzhaki, Noncommutative Yang-Mills and the AdS/CFT correspondence, Phys. Lett. B 465 (1999) 142 [hep-th/9907166] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. J.M. Maldacena and J.G. Russo, Large-N limit of noncommutative gauge theories, JHEP 09 (1999) 025 [hep-th/9908134] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. 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].

    MathSciNet  ADS  Google Scholar 

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

    MathSciNet  ADS  MATH  Google Scholar 

  18. E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  19. G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  20. J.I. Kapusta and C. Gale, Finite-temperature field theory: principles and applications, Cambridge University Press, Cambridge U.K. (2006)

    Book  MATH  Google Scholar 

  21. M. Le Bellac. Thermal field theory, Cambridge University Press, Cambridge U.K. (1996).

    Book  Google Scholar 

  22. D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].

    ADS  Google Scholar 

  25. E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. N. Ishibashi, S. Iso, H. Kawai and Y. Kitazawa, Wilson loops in noncommutative Yang-Mills, Nucl. Phys. B 573 (2000) 573 [hep-th/9910004] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. S.R. Das and S.-J. Rey, Open Wilson lines in noncommutative gauge theory and tomography of holographic dual supergravity, Nucl. Phys. B 590 (2000) 453 [hep-th/0008042] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. D.J. Gross, A. Hashimoto and N. Itzhaki, Observables of noncommutative gauge theories, Adv. Theor. Math. Phys. 4 (2000) 893 [hep-th/0008075] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  29. O. Aharony, M. Berkooz, D. Kutasov and N. Seiberg, Linear dilatons, NS five-branes and holography, JHEP 10 (1998) 004 [hep-th/9808149] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. S. Minwalla and N. Seiberg, Comments on the IIA (NS)five-brane, JHEP 06 (1999) 007 [hep-th/9904142] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. S.R. Das and B. Ghosh, A note on supergravity duals of noncommutative Yang-Mills theory, JHEP 06 (2000) 043 [hep-th/0005007] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. E.W. Leaver, Quasinormal modes of Reissner-Nordstrom black holes, Phys. Rev. D 41 (1990) 2986 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. J.H. Schwarz, Covariant field equations of chiral N = 2 D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [INSPIRE].

    Article  ADS  Google Scholar 

  34. H. Liu, *-Trek II: *(n) operations, open Wilson lines and the Seiberg-Witten map, Nucl. Phys. B 614 (2001) 305 [hep-th/0011125] [INSPIRE].

    Article  ADS  Google Scholar 

  35. H. Liu and J. Michelson, Supergravity couplings of noncommutative D-branes, Nucl. Phys. B 615 (2001) 169 [hep-th/0101016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. S.R. Das and S.P. Trivedi, Supergravity couplings to noncommutative branes, open Wilson lines and generalized star products, JHEP 02 (2001) 046 [hep-th/0011131] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. C.-S. Chu and C.M. Ho, Nonequilibrium dynamics in noncommutative spacetime, JHEP 02 (2010) 098 [arXiv:0912.1748] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. S. Minwalla, M. Van Raamsdonk and N. Seiberg, Noncommutative perturbative dynamics, JHEP 02 (2000) 020 [hep-th/9912072] [INSPIRE].

    Article  ADS  Google Scholar 

  39. M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. T. Banks, W. Fischler, S. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  41. A. Connes, M.R. Douglas and A.S. Schwarz, Noncommutative geometry and matrix theory: compactification on tori, JHEP 02 (1998) 003 [hep-th/9711162] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Walter Tangarife Garcia.

Additional information

ArXiv ePrint: 1204.5748

Rights and permissions

Reprints and permissions

About this article

Cite this article

Edalati, M., Fischler, W., Pedraza, J.F. et al. Fast scramblers and non-commutative gauge theories. J. High Energ. Phys. 2012, 43 (2012). https://doi.org/10.1007/JHEP07(2012)043

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP07(2012)043

Keywords

Navigation