Abstract
We argue that the usual notions of thermodynamic and entanglement entropy have novel analogs in the context of higher spin theories. In particular, the Wald and RyuTakayanagi formulas have natural higher spin extensions that we work out and study. On the CFT side, just as standard entanglement entropy in CFT2 can be computed from twist field correlators, we demonstrate that by introducing corresponding operators carrying higher spin charge we can precisely reproduce our results from the bulk.
We also show that the first law for entanglement entropy implies the linearized field equations for the metric and higher spin fields, generalizing recent work on deriving the linearized Einstein equations from the first law.
Article PDF
Similar content being viewed by others
References
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S.F. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, An AdS 3 dual for minimal model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
T. Faulkner, M. Guica, T. Hartman, R.C. Myers and M. Van Raamsdonk, Gravitation from entanglement in holographic CFTs, JHEP 03 (2014) 051 [arXiv:1312.7856] [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].
M. Ammon, A. Castro and N. Iqbal, Wilson lines and entanglement entropy in higher spin gravity, JHEP 10 (2013) 110 [arXiv:1306.4338] [INSPIRE].
J. de Boer and J.I. Jottar, Entanglement entropy and higher spin holography in AdS 3, JHEP 04 (2014) 089 [arXiv:1306.4347] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 06 (2004) P06002 [hep-th/0405152] [INSPIRE].
N. Lashkari, M.B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ‘thermodynamics’, JHEP 04 (2014) 195 [arXiv:1308.3716] [INSPIRE].
B. Swingle and M. Van Raamsdonk, Universality of gravity from entanglement, arXiv:1405.2933 [INSPIRE].
E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
A. Achucarro and P.K. Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
J. de Boer and J.I. Jottar, Thermodynamics of higher spin black holes in AdS 3, JHEP 01 (2014) 023 [arXiv:1302.0816] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
M. Gutperle and P. Kraus, Higher spin black holes, JHEP 05 (2011) 022 [arXiv:1103.4304] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Spacetime geometry in higher spin gravity, JHEP 10 (2011) 053 [arXiv:1106.4788] [INSPIRE].
A. Castro, E. Hijano, A. Lepage-Jutier and A. Maloney, Black holes and singularity resolution in higher spin gravity, JHEP 01 (2012) 031 [arXiv:1110.4117] [INSPIRE].
H.-S. Tan, Aspects of three-dimensional spin-4 gravity, JHEP 02 (2012) 035 [arXiv:1111.2834] [INSPIRE].
M.R. Gaberdiel, T. Hartman and K. Jin, Higher spin black holes from CFT, JHEP 04 (2012) 103 [arXiv:1203.0015] [INSPIRE].
M. Bañados, R. Canto and S. Theisen, The action for higher spin black holes in three dimensions, JHEP 07 (2012) 147 [arXiv:1204.5105] [INSPIRE].
A. Perez, D. Tempo and R. Troncoso, Higher spin gravity in 3D: black holes, global charges and thermodynamics, Phys. Lett. B 726 (2013) 444 [arXiv:1207.2844] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Towards metric-like higher-spin gauge theories in three dimensions, J. Phys. A 46 (2013) 214017 [arXiv:1208.1851] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Black holes in three dimensional higher spin gravity: a review, J. Phys. A 46 (2013) 214001 [arXiv:1208.5182] [INSPIRE].
P. Kraus and E. Perlmutter, Partition functions of higher spin black holes and their CFT duals, JHEP 11 (2011) 061 [arXiv:1108.2567] [INSPIRE].
P. Kraus and E. Perlmutter, Probing higher spin black holes, JHEP 02 (2013) 096 [arXiv:1209.4937] [INSPIRE].
B. Chen, J. Long and Y.-N. Wang, Black holes in truncated higher spin AdS 3 gravity, JHEP 12 (2012) 052 [arXiv:1209.6185] [INSPIRE].
J.R. David, M. Ferlaino and S.P. Kumar, Thermodynamics of higher spin black holes in 3D, JHEP 11 (2012) 135 [arXiv:1210.0284] [INSPIRE].
B. Chen, J. Long and Y.-N. Wang, Phase structure of higher spin black hole, JHEP 03 (2013) 017 [arXiv:1212.6593] [INSPIRE].
A. Perez, D. Tempo and R. Troncoso, Higher spin black hole entropy in three dimensions, JHEP 04 (2013) 143 [arXiv:1301.0847] [INSPIRE].
P. Kraus and T. Ugajin, An entropy formula for higher spin black holes via conical singularities, JHEP 05 (2013) 160 [arXiv:1302.1583] [INSPIRE].
S. Datta and J.R. David, Black holes in higher spin supergravity, JHEP 07 (2013) 110 [arXiv:1303.1946] [INSPIRE].
M. Ferlaino, T. Hollowood and S.P. Kumar, Asymptotic symmetries and thermodynamics of higher spin black holes in AdS 3, Phys. Rev. D 88 (2013) 066010 [arXiv:1305.2011] [INSPIRE].
G. Compére and W. Song, \( \mathcal{W} \) symmetry and integrability of higher spin black holes, JHEP 09 (2013) 144 [arXiv:1306.0014] [INSPIRE].
M.R. Gaberdiel, K. Jin and E. Perlmutter, Probing higher spin black holes from CFT, JHEP 10 (2013) 045 [arXiv:1307.2221] [INSPIRE].
G. Compére, J.I. Jottar and W. Song, Observables and microscopic entropy of higher spin black holes, JHEP 11 (2013) 054 [arXiv:1308.2175] [INSPIRE].
W. Li, F.-L. Lin and C.-W. Wang, Modular properties of 3D higher spin theory, JHEP 12 (2013) 094 [arXiv:1308.2959] [INSPIRE].
M. Henneaux, A. Perez, D. Tempo and R. Troncoso, Chemical potentials in three-dimensional higher spin anti-de Sitter gravity, JHEP 12 (2013) 048 [arXiv:1309.4362] [INSPIRE].
M. Gutperle, E. Hijano and J. Samani, Lifshitz black holes in higher spin gravity, JHEP 04 (2014) 020 [arXiv:1310.0837] [INSPIRE].
M. Beccaria and G. Macorini, On the partition functions of higher spin black holes, JHEP 12 (2013) 027 [arXiv:1310.4410] [INSPIRE].
M. Beccaria and G. Macorini, Resummation of scalar correlator in higher spin black hole background, JHEP 02 (2014) 071 [arXiv:1311.5450] [INSPIRE].
M. Beccaria and G. Macorini, Analysis of higher spin black holes with spin-4 chemical potential, JHEP 07 (2014) 047 [arXiv:1312.5599] [INSPIRE].
A. Chowdhury and A. Saha, Phase structure of higher spin black holes, arXiv:1312.7017 [INSPIRE].
S. Datta, J.R. David, M. Ferlaino and S.P. Kumar, Higher spin entanglement entropy from CFT, JHEP 06 (2014) 096 [arXiv:1402.0007] [INSPIRE].
C. Bunster, M. Henneaux, A. Perez, D. Tempo and R. Troncoso, Generalized black holes in three-dimensional spacetime, JHEP 05 (2014) 031 [arXiv:1404.3305] [INSPIRE].
S. Datta, J.R. David, M. Ferlaino and S.P. Kumar, A universal correction to higher spin entanglement entropy, Phys. Rev. D 90 (2014) 041903 [arXiv:1405.0015] [INSPIRE].
S. Datta, Relative entropy in higher spin holography, arXiv:1406.0520 [INSPIRE].
J.L. Cardy, Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270 (1986) 186 [INSPIRE].
T. Faulkner, The entanglement Rényi entropies of disjoint intervals in AdS/CFT, arXiv:1303.7221 [INSPIRE].
A. Castro, R. Gopakumar, M. Gutperle and J. Raeymaekers, Conical defects in higher spin theories, JHEP 02 (2012) 096 [arXiv:1111.3381] [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: 1406.1804
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
Hijano, E., Kraus, P. A new spin on entanglement entropy. J. High Energ. Phys. 2014, 41 (2014). https://doi.org/10.1007/JHEP12(2014)041
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2014)041