Skip to main content
SpringerLink
Log in

Strongly coupled gauge theories: high and low temperature behavior of non-local observables

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

Abstract

We explore the high and low temperature behavior of non-local observables in strongly coupled gauge theories that are dual to AdS. We develop a systematic expansion for equal time two-point correlation, spatial Wilson loops and entanglement entropy at finite temperature using the AdS/CFT correspondence, leading to analytic expressions for these observables at high and low temperature limits. This approach enables the identification of the contributions of different regions of the bulk geometry to these gauge theory observables.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Dine and W. Fischler, The thermodynamics of the nonlinear σ-model: a toy for high temperature qcd, Phys. Lett. B 105 (1981) 207 [INSPIRE].

    ADS  Google Scholar 

  2. D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and Instantons at Finite Temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. H.A. Weldon, Covariant Calculations at Finite Temperature: The Relativistic Plasma, Phys. Rev. D 26 (1982) 1394 [INSPIRE].

    ADS  Google Scholar 

  4. N. Landsman and C. van Weert, Real and Imaginary Time Field Theory at Finite Temperature and Density, Phys. Rept. 145 (1987) 141 [INSPIRE].

    Article  ADS  Google Scholar 

  5. E. Braaten and R.D. Pisarski, Soft Amplitudes in Hot Gauge Theories: A General Analysis, Nucl. Phys. B 337 (1990) 569 [INSPIRE].

    Article  ADS  Google Scholar 

  6. 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 

  7. S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity, Nucl. Phys. B 527 (1998) 171 [hep-th/9803135] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. E. Shuryak, Physics of Strongly coupled quark-gluon Plasma, Prog. Part. Nucl. Phys. 62 (2009) 48 [arXiv:0807.3033] [INSPIRE].

    Article  ADS  Google Scholar 

  9. M. Panero, Thermodynamics of the QCD plasma and the large-N limit, Phys. Rev. Lett. 103 (2009) 232001 [arXiv:0907.3719] [INSPIRE].

    Article  ADS  Google Scholar 

  10. E. Megias, H. Pirner and K. Veschgini, QCD thermodynamics using five-dimensional gravity, Phys. Rev. D 83 (2011) 056003 [arXiv:1009.2953] [INSPIRE].

    ADS  Google Scholar 

  11. M. Mojaza, C. Pica and F. Sannino, Hot Conformal Gauge Theories, Phys. Rev. D 82 (2010) 116009 [arXiv:1010.4798] [INSPIRE].

    ADS  Google Scholar 

  12. P. Petreczky, Lattice QCD at non-zero temperature, J. Phys. G 39 (2012) 093002 [arXiv:1203.5320] [INSPIRE].

    ADS  Google Scholar 

  13. 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] [INSPIRE].

  14. 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 

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

    MathSciNet  ADS  MATH  Google Scholar 

  16. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. L. Susskind and E. Witten, The Holographic bound in anti-de Sitter space, hep-th/9805114 [INSPIRE].

  18. 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 

  19. C. Herzog and D. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [INSPIRE].

    Article  ADS  Google Scholar 

  21. V.E. Hubeny, Extremal surfaces as bulk probes in AdS/CFT, JHEP 07 (2012) 093 [arXiv:1203.1044] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].

  23. V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev. D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  24. J. Louko, D. Marolf and S.F. Ross, On geodesic propagators and black hole holography, Phys. Rev. D 62 (2000) 044041 [hep-th/0002111] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  25. L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The Black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. G. Festuccia and H. Liu, Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I., JHEP 04 (2006) 044 [hep-th/0506202] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops in the large-N limit at finite temperature, Phys. Lett. B 434 (1998) 36 [hep-th/9803137] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  29. A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops, confinement and phase transitions in large-N gauge theories from supergravity, JHEP 06 (1998) 001 [hep-th/9803263] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE].

  31. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: An Overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].

    MathSciNet  Google Scholar 

  34. L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin, A Quantum Source of Entropy for Black Holes, Phys. Rev. D 34 (1986) 373 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  35. M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. H. Casini, Geometric entropy, area and strong subadditivity, Class. Quant. Grav. 21 (2004) 2351 [hep-th/0312238] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. M. Plenio, J. Eisert, J. Dreissig and M. Cramer, Entropy, entanglement and area: analytical results for harmonic lattice systems, Phys. Rev. Lett. 94 (2005) 060503 [quant-ph/0405142] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. M. Cramer, J. Eisert, M. Plenio and J. Dreissig, An Entanglement-area law for general bosonic harmonic lattice systems, Phys. Rev. A 73 (2006) 012309 [quant-ph/0505092] [INSPIRE].

    ADS  Google Scholar 

  39. S. Das and S. Shankaranarayanan, How robust is the entanglement entropy: Area relation?, Phys. Rev. D 73 (2006) 121701 [gr-qc/0511066] [INSPIRE].

    ADS  Google Scholar 

  40. C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].

    Article  Google Scholar 

  42. I. Bah, A. Faraggi, L.A. Pando Zayas and C.A. Terrero-Escalante, Holographic entanglement entropy and phase transitions at finite temperature, Int. J. Mod. Phys. A 24 (2009) 2703 [arXiv:0710.5483] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  43. S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  44. L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].

    ADS  Google Scholar 

  45. M. Alishahiha, E. O Colgain and H. Yavartanoo, Charged Black Branes with Hyperscaling Violating Factor, JHEP 11 (2012) 137 [arXiv:1209.3946] [INSPIRE].

    Article  ADS  Google Scholar 

  46. X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].

    Article  ADS  Google Scholar 

  47. W. Fischler, A. Kundu and S. Kundu, Holographic Mutual Information at Finite Temperature, arXiv:1212.4764 [INSPIRE].

  48. S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. M.M. Wolf, F. Verstraete, M.B. Hastings and J.I. Cirac, Area Laws in Quantum Systems: Mutual Information and Correlations, Physical Review Letters 100 (2008), no. 7 070502 [arXiv:0704.3906].

    Article  MathSciNet  ADS  Google Scholar 

  50. J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].

    Article  ADS  Google Scholar 

  51. J. Aparicio and E. Lopez, Evolution of Two-Point Functions from Holography, JHEP 12 (2011) 082 [arXiv:1109.3571] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. T. Albash and C.V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys. 13 (2011) 045017 [arXiv:1008.3027] [INSPIRE].

    Article  ADS  Google Scholar 

  53. V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps et al., Thermalization of Strongly Coupled Field Theories, Phys. Rev. Lett. 106 (2011) 191601 [arXiv:1012.4753] [INSPIRE].

    Article  ADS  Google Scholar 

  54. V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].

    ADS  Google Scholar 

  55. D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [arXiv:1205.1548] [INSPIRE].

    Article  ADS  Google Scholar 

  56. E. Caceres and A. Kundu, Holographic Thermalization with Chemical Potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theory Group, Department of Physics, University of Texas, Austin, TX, 78712, U.S.A.

    Willy Fischler & Sandipan Kundu

  2. Texas Cosmology Center, University of Texas, Austin, TX, 78712, U.S.A.

    Willy Fischler & Sandipan Kundu

Authors
  1. Willy Fischler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sandipan Kundu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sandipan Kundu.

Additional information

ArXiv ePrint: 1212.2643

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fischler, W., Kundu, S. Strongly coupled gauge theories: high and low temperature behavior of non-local observables. J. High Energ. Phys. 2013, 98 (2013). https://doi.org/10.1007/JHEP05(2013)098

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2013)098

Keywords

Search

Navigation