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Journal of High Energy Physics

, 2013:19 | Cite as

Entanglement and thermal entropy of gauge fields

  • Christopher ElingEmail author
  • Yaron Oz
  • Stefan Theisen
Article

Abstract

We consider the universal logarithmic divergent term in the entanglement entropy of gauge fields in the Minkowski vacuum with an entangling sphere. Employing the mapping in arXiv:1102.0440, we analyze the corresponding thermal entropy on open Einstein universe and on the static patch of de Sitter. Using the heat kernel of the vector Laplacian we resolve a discrepancy between the free field calculation and the expected Euler conformal anomaly. The resolution suggests a modification of the well known formulas for the vacuum expectation value of the spin-1 energy-momentum tensor on conformally flat space-times.

Keywords

AdS-CFT Correspondence Gauge Symmetry Conformal and W Symmetry Anomalies in Field and String Theories 

References

  1. [1]
    H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    P. Candelas and J. Dowker, Field theories on conformally related space-times: some global considerations, Phys. Rev. D 19 (1979) 2902 [INSPIRE].MathSciNetADSGoogle Scholar
  3. [3]
    C.G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [hep-th/9401072] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    J. Dowker, Entanglement entropy for even spheres, arXiv:1009.3854 [INSPIRE].
  6. [6]
    D.N. Kabat, Black hole entropy and entropy of entanglement, Nucl. Phys. B 453 (1995) 281 [hep-th/9503016] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, JHEP 06 (1999) 036 [hep-th/9906040] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    M. Brown, A. Ottewill and D.N. Page, Conformally Invariant Quantum Field Theory in Static Einstein Space-times, Phys. Rev. D 33 (1986) 2840 [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    L.S. Brown and J.P. Cassidy, Stress Tensors and their Trace Anomalies in Conformally Flat Space-Times, Phys. Rev. D 16 (1977) 1712 [INSPIRE].ADSGoogle Scholar
  10. [10]
    T. Bunch and P. Davies, Quantum Field Theory in de Sitter Space: Renormalization by Point Splitting, Proc. Roy. Soc. Lond. A 360 (1978) 117 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    S. Christensen and M. Duff, New Gravitational Index Theorems and Supertheorems, Nucl. Phys. B 154 (1979) 301 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    L. De Nardo, D.V. Fursaev and G. Miele, Heat kernel coefficients and spectra of the vector Laplacians on spherical domains with conical singularities, Class. Quant. Grav. 14 (1997) 1059 [hep-th/9610011] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  13. [13]
    D.V. Fursaev and S.N. Solodukhin, On the description of the iemannian geometry in the presence of conical defects, Phys. Rev. D 52 (1995) 2133 [hep-th/9501127] [INSPIRE].MathSciNetADSGoogle Scholar
  14. [14]
    I. Arav and Y. Oz, The Sound of Topology in the AdS/CFT Correspondence, JHEP 11 (2012) 014 [arXiv:1206.5936] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    D. Marolf, M. Rangamani and M. Van Raamsdonk, Holographic models of de Sitter QFTs, Class. Quant. Grav. 28 (2011) 105015 [arXiv:1007.3996] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    S.S. Gubser, Einstein manifolds and conformal field theories, Phys. Rev. D 59 (1999) 025006 [hep-th/9807164] [INSPIRE].MathSciNetADSGoogle Scholar
  17. [17]
    P. Candelas and D. Deutsch, On the vacuum stress induced by uniform acceleration or supporting the ether, Proc. Roy. Soc. Lond. A 354 (1977) 79 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    V.P. Frolov and E. Serebryanyi, Vacuum Polarization in the Gravitational Field of a Cosmic String, Phys. Rev. D 35 (1987) 3779 [INSPIRE].ADSGoogle Scholar
  19. [19]
    J. Dowker, Vacuum Averages for Arbitrary Spin Around a Cosmic String, Phys. Rev. D 36 (1987) 3742 [INSPIRE].ADSGoogle Scholar
  20. [20]
    B. Allen, J. McLaughlin and A. Ottewill, Photon and graviton Greens functions on cosmic string space-times, Phys. Rev. D 45 (1992) 4486 [INSPIRE].MathSciNetADSGoogle Scholar
  21. [21]
    V. Moretti and L. Vanzo, Thermal Wightman functions and renormalized stress tensors in the Rindler wedge, Phys. Lett. B 375 (1996) 54 [hep-th/9507139] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    M. Yamazaki, Entanglement in Theory Space, Europhys. Lett. 103 (2013) 21002 [arXiv:1304.0762] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    D. Kabat and D. Sarkar, Cosmic string interactions induced by gauge and scalar fields, Phys. Rev. D 86 (2012) 084021 [arXiv:1206.5642] [INSPIRE].ADSGoogle Scholar
  24. [24]
    W. Donnelly and A.C. Wall, Do gauge fields really contribute negatively to black hole entropy?, Phys. Rev. D 86 (2012) 064042 [arXiv:1206.5831] [INSPIRE].ADSGoogle Scholar
  25. [25]
    D. Iellici and V. Moretti, Thermal partition function of photons and gravitons in a Rindler wedge, Phys. Rev. D 54 (1996) 7459 [hep-th/9607015] [INSPIRE].MathSciNetADSGoogle Scholar
  26. [26]
    S.N. Solodukhin, Remarks on effective action and entanglement entropy of Maxwell field in generic gauge, JHEP 12 (2012) 036 [arXiv:1209.2677] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    V. Moretti, Direct zeta function approach and renormalization of one loop stress tensors in curved space-times, Phys. Rev. D 56 (1997) 7797 [hep-th/9705060] [INSPIRE].MathSciNetADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Max Planck Institute for Gravitational PhysicsAlbert Einstein InstitutePotsdamGermany
  2. 2.Raymond and Beverly Sackler School of Physics and AstronomyTel Aviv UniversityTel AvivIsrael

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