Abstract
In this paper we show that in addition to the known minimal surfaces which appear in the literature for computing the holographic entanglement entropy, there are other minimal surfaces with non-zero extrinsic curvature. We use the approach of regularization procedure presented by Fursaev et al. in [7], to compute the quadratic and cubic curvature invariants on manifolds with squashed cones. The results can be used to find the leading and universal terms of the holographic entanglement entropy to understand which solution corresponds to the actual minimal entropy.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
A. Bhattacharyya, A. Kaviraj and A. Sinha, Entanglement entropy in higher derivative holography, JHEP 08 (2013) 012 [arXiv:1305.6694] [INSPIRE].
T. Jacobson and R.C. Myers, Black hole entropy and higher curvature interactions, Phys. Rev. Lett. 70 (1993) 3684 [hep-th/9305016] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, On holographic entanglement entropy and higher curvature gravity, JHEP 04 (2011) 025 [arXiv:1101.5813] [INSPIRE].
D.V. Fursaev, A. Patrushev and S.N. Solodukhin, Distributional geometry of squashed cones, Phys. Rev. D 88 (2013) 044054 [arXiv:1306.4000] [INSPIRE].
D.V. Fursaev and S.N. Solodukhin, On the description of the Riemannian geometry in the presence of conical defects, Phys. Rev. D 52 (1995) 2133 [hep-th/9501127] [INSPIRE].
A. Bhattacharyya, M. Sharma and A. Sinha, On generalized gravitational entropy, squashed cones and holography, JHEP 01 (2014) 021 [arXiv:1308.5748] [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, JHEP 03 (2014) 070 [arXiv:1310.6659] [INSPIRE].
M. Alishahiha, A.F. Astaneh and M.R.M. Mozaffar, Entanglement entropy for logarithmic conformal field theory, Phys. Rev. D 89 (2014) 065023 [arXiv:1310.4294] [INSPIRE].
J. Erdmenger, M. Flory and C. Sleight, Conditions on holographic entangling surfaces in higher curvature gravity, JHEP 06 (2014) 104 [arXiv:1401.5075] [INSPIRE].
A. Bhattacharyya and M. Sharma, On entanglement entropy functionals in higher derivative gravity theories, JHEP 10 (2014) 130 [arXiv:1405.3511] [INSPIRE].
P. Bueno and P.F. Ramirez, Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation, JHEP 12 (2014) 078 [arXiv:1408.6380] [INSPIRE].
R.-X. Miao and W.-Z. Guo, Holographic entanglement entropy for the most general higher derivative gravity, JHEP 08 (2015) 031 [arXiv:1411.5579] [INSPIRE].
W.-Z. Guo and R.-X. Miao, Entropy for gravitational Chern-Simons terms by squashed cone method, arXiv:1506.08397 [INSPIRE].
T. Azeyanagi, R. Loganayagam and G.S. Ng, Holographic entanglement for Chern-Simons terms, arXiv:1507.02298 [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
A. Sinha, On the new massive gravity and AdS/CFT, JHEP 06 (2010) 061 [arXiv:1003.0683] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP 08 (2010) 035 [arXiv:1004.2055] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1508.02527
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Ghodsi, A., Moghadassi, M. Holographic entanglement entropy from minimal surfaces with/without extrinsic curvature. J. High Energ. Phys. 2016, 37 (2016). https://doi.org/10.1007/JHEP02(2016)037
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)037