Abstract
Using the proposal for holographic entanglement entropy in higher derivative gravities, we compute holographic entanglement entropy for the conformal gravity in four dimensions which turns out to be finite. However, if one subtracts the contribution of the four dimensional Gauss-Bonnet term, the corresponding entanglement entropy has a divergent term and indeed restricted to an Einstein solution of the conformal gravity, the resultant entanglement entropy is exactly the same as that in the Einstein gravity. We will also make a comment on the first law of the entanglement thermodynamics for the conformal gravity in four dimensions.
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References
K. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
S.L. Adler, Einstein gravity as a symmetry breaking effect in quantum field theory, Rev. Mod. Phys. 54 (1982) 729 [Erratum ibid. 55 (1983) 837] [INSPIRE].
J. Maldacena, Einstein gravity from conformal gravity, arXiv:1105.5632 [INSPIRE].
M.T. Anderson, L 2 curvature and volume renormalization of AHE metrics on 4-manifolds, Math. Res. Lett. 8 (2001) 171 [math/0011051].
R.J. Riegert, Birkhoff ’s theorem in conformal gravity, Phys. Rev. Lett. 53 (1984) 315 [INSPIRE].
D. Grumiller, Model for gravity at large distances, Phys. Rev. Lett. 105 (2010) 211303 [Erratum ibid. 106 (2011) 039901] [arXiv:1011.3625] [INSPIRE].
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].
M. Alishahiha and R. Fareghbal, D-dimensional log gravity, Phys. Rev. D 83 (2011) 084052 [arXiv:1101.5891] [INSPIRE].
I. Gullu, M. Gurses, T.C. Sisman and B. Tekin, AdS waves as exact solutions to quadratic gravity, Phys. Rev. D 83 (2011) 084015 [arXiv:1102.1921] [INSPIRE].
H. Lü, Y. Pang, C.N. Pope and J.F. Vazquez-Poritz, AdS and Lifshitz black holes in conformal and Einstein-Weyl gravities, Phys. Rev. D 86 (2012) 044011 [arXiv:1204.1062] [INSPIRE].
D. Grumiller, M. Irakleidou, I. Lovrekovic and R. McNees, Conformal gravity holography in four dimensions, arXiv:1310.0819 [INSPIRE].
A. Naseh, unpublished.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
D.V. Fursaev, A. Patrushev and S.N. Solodukhin, Distributional geometry of squashed cones, arXiv:1306.4000 [INSPIRE].
A. Bhattacharyya, M. Sharma and A. Sinha, On generalized gravitational entropy, squashed cones and holography, JHEP 01 (2014) 021 [arXiv:1308.5748] [INSPIRE].
M. Alishahiha, A.F. Astaneh and M.R.M. Mozaffar, Entanglement entropy for logarithmic conformal field theory, arXiv:1310.4294 [INSPIRE].
X. Dong, Holographic entanglement entropy for general higher derivative gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
J. Camps, Generalized entropy and higher derivative Gravity, arXiv:1310.6659 [INSPIRE].
J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, Thermodynamical property of entanglement entropy for excited states, Phys. Rev. Lett. 110 (2013) 091602 [arXiv:1212.1164] [INSPIRE].
O. Mišković and R. Olea, Topological regularization and self-duality in four-dimensional Anti-de Sitter gravity, Phys. Rev. D 79 (2009) 124020 [arXiv:0902.2082] [INSPIRE].
R. Olea, Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes, JHEP 06 (2005) 023 [hep-th/0504233] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
K. Narayan, T. Takayanagi and S.P. Trivedi, AdS plane waves and entanglement entropy, JHEP 04 (2013) 051 [arXiv:1212.4328] [INSPIRE].
D. Allahbakhshi, M. Alishahiha and A. Naseh, Entanglement thermodynamics, JHEP 08 (2013) 102 [arXiv:1305.2728] [INSPIRE].
D.D. Blanco, H. Casini, L.-Y. Hung and R.C. Myers, Relative entropy and holography, JHEP 08 (2013) 060 [arXiv:1305.3182] [INSPIRE].
G. Wong, I. Klich, L.A. Pando Zayas and D. Vaman, Entanglement temperature and entanglement entropy of excited states, JHEP 12 (2013) 020 [arXiv:1305.3291] [INSPIRE].
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ArXiv ePrint: 1311.4329
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Alishahiha, M., Faraji Astaneh, A. & Mohammadi Mozaffar, M.R. Holographic entanglement entropy for 4D conformal gravity. J. High Energ. Phys. 2014, 8 (2014). https://doi.org/10.1007/JHEP02(2014)008
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DOI: https://doi.org/10.1007/JHEP02(2014)008