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.
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References
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
P. Candelas and J. Dowker, Field theories on conformally related space-times: some global considerations, Phys. Rev. D 19 (1979) 2902 [INSPIRE].
C.G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [hep-th/9401072] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
J. Dowker, Entanglement entropy for even spheres, arXiv:1009.3854 [INSPIRE].
D.N. Kabat, Black hole entropy and entropy of entanglement, Nucl. Phys. B 453 (1995) 281 [hep-th/9503016] [INSPIRE].
R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, JHEP 06 (1999) 036 [hep-th/9906040] [INSPIRE].
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].
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].
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].
S. Christensen and M. Duff, New Gravitational Index Theorems and Supertheorems, Nucl. Phys. B 154 (1979) 301 [INSPIRE].
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].
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].
I. Arav and Y. Oz, The Sound of Topology in the AdS/CFT Correspondence, JHEP 11 (2012) 014 [arXiv:1206.5936] [INSPIRE].
D. Marolf, M. Rangamani and M. Van Raamsdonk, Holographic models of de Sitter QFTs, Class. Quant. Grav. 28 (2011) 105015 [arXiv:1007.3996] [INSPIRE].
S.S. Gubser, Einstein manifolds and conformal field theories, Phys. Rev. D 59 (1999) 025006 [hep-th/9807164] [INSPIRE].
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].
V.P. Frolov and E. Serebryanyi, Vacuum Polarization in the Gravitational Field of a Cosmic String, Phys. Rev. D 35 (1987) 3779 [INSPIRE].
J. Dowker, Vacuum Averages for Arbitrary Spin Around a Cosmic String, Phys. Rev. D 36 (1987) 3742 [INSPIRE].
B. Allen, J. McLaughlin and A. Ottewill, Photon and graviton Green’s functions on cosmic string space-times, Phys. Rev. D 45 (1992) 4486 [INSPIRE].
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].
M. Yamazaki, Entanglement in Theory Space, Europhys. Lett. 103 (2013) 21002 [arXiv:1304.0762] [INSPIRE].
D. Kabat and D. Sarkar, Cosmic string interactions induced by gauge and scalar fields, Phys. Rev. D 86 (2012) 084021 [arXiv:1206.5642] [INSPIRE].
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].
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].
S.N. Solodukhin, Remarks on effective action and entanglement entropy of Maxwell field in generic gauge, JHEP 12 (2012) 036 [arXiv:1209.2677] [INSPIRE].
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].
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ArXiv ePrint: 1308.4964
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Eling, C., Oz, Y. & Theisen, S. Entanglement and thermal entropy of gauge fields. J. High Energ. Phys. 2013, 19 (2013). https://doi.org/10.1007/JHEP11(2013)019
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DOI: https://doi.org/10.1007/JHEP11(2013)019