Abstract
We compute holographic Rényi entropies for spherical entangling surfaces on the boundary while considering third order Lovelock gravity with negative cosmological constant in the bulk. Our study shows that third order Lovelock black holes with hyperbolic event horizon are unstable, and at low temperatures those with smaller mass are favoured, giving rise to first order phase transitions in the bulk. We determine regions in the Lovelock parameter space in arbitrary dimensions, where bulk phase transitions happen and where boundary causality constraints are met. We show that each of these points corresponds to a dual boundary conformal field theory whose Rényi entropy exhibits a kink at a certain critical index n.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory: A non-technical introduction, Int. J. Quant. Inf. 4 (2006) 429 [quant-ph/0505193] [INSPIRE].
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
E. Perlmutter, A universal feature of CFT Rényi entropy, JHEP 03 (2014) 117 [arXiv:1308.1083] [INSPIRE].
X. Dong, Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories, Phys. Rev. Lett. 116 (2016) 251602 [arXiv:1602.08493] [INSPIRE].
D.A. Abanin and E. Demler, Measuring entanglement entropy of a generic many-body system with a quantum switch, Phys. Rev. Lett. 109 (2012) 020504 [arXiv:1204.2819].
A.J. Daley, H. Pichler, J. Schachenmayer and P. Zoller, Measuring entanglement growth in quench dynamics of bosons in an optical lattice, Phys. Rev. Lett. 109 (2012) 020505 [arXiv:1205.1521].
R. Islam et al., Measuring entanglement entropy through the interference of quantum many-body twins, arXiv:1509.01160.
C.G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333 (1994) 55 [hep-th/9401072] [INSPIRE].
C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B 424 (1994) 443 [hep-th/9403108] [INSPIRE].
J.L. Cardy, O.A. Castro-Alvaredo and B. Doyon, Form factors of branch-point twist fields in quantum integrable models and entanglement entropy, J. Statist. Phys. 130 (2008) 129 [arXiv:0706.3384] [INSPIRE].
D.V. Fursaev, Proof of the holographic formula for entanglement entropy, JHEP 09 (2006) 018 [hep-th/0606184] [INSPIRE].
M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
X. Dong, A. Lewkowycz and M. Rangamani, Deriving covariant holographic entanglement, JHEP 11 (2016) 028 [arXiv:1607.07506] [INSPIRE].
M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, Lect. Notes Phys. 931 (2017) 1 [arXiv:1609.01287] [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. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
X. Dong, The Gravity Dual of Renyi Entropy, Nature Commun. 7 (2016) 12472 [arXiv:1601.06788] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
L.-Y. Hung, R.C. Myers, M. Smolkin and A. Yale, Holographic Calculations of Renyi Entropy, JHEP 12 (2011) 047 [arXiv:1110.1084] [INSPIRE].
M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, Twist operators in higher dimensions, JHEP 10 (2014) 178 [arXiv:1407.6429] [INSPIRE].
C.-S. Chu and R.-X. Miao, Universality in the shape dependence of holographic Rényi entropy for general higher derivative gravity, JHEP 12 (2016) 036 [arXiv:1608.00328] [INSPIRE].
L. Bianchi, S. Chapman, X. Dong, D.A. Galante, M. Meineri and R.C. Myers, Shape dependence of holographic Rényi entropy in general dimensions, JHEP 11 (2016) 180 [arXiv:1607.07418] [INSPIRE].
J. Camps, Gravity duals of boundary cones, JHEP 09 (2016) 139 [arXiv:1605.08588] [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].
J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Entanglement Entropy in Lovelock Gravities, JHEP 07 (2011) 109 [arXiv:1101.5781] [INSPIRE].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [arXiv:1006.1263] [INSPIRE].
R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP 01 (2011) 125 [arXiv:1011.5819] [INSPIRE].
N. Ogawa and T. Takayanagi, Higher Derivative Corrections to Holographic Entanglement Entropy for AdS Solitons, JHEP 10 (2011) 147 [arXiv:1107.4363] [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].
D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498 [INSPIRE].
D. Lovelock, Divergence-free tensorial concomitants, Aequat. Math. 4 (1970) 127.
B. Zwiebach, Curvature Squared Terms and String Theories, Phys. Lett. B 156 (1985) 315 [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Order alpha-prime (Two Loop) Equivalence of the String Equations of Motion and the σ-model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor, Nucl. Phys. B 293 (1987) 385 [INSPIRE].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].
J. de Boer, M. Kulaxizi and A. Parnachev, AdS 7 /CF T 6 , Gauss-Bonnet Gravity and Viscosity Bound, JHEP 03 (2010) 087 [arXiv:0910.5347] [INSPIRE].
X.O. Camanho, J.D. Edelstein and M.F. Paulos, Lovelock theories, holography and the fate of the viscosity bound, JHEP 05 (2011) 127 [arXiv:1010.1682] [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
X.O. Camanho and J.D. Edelstein, Causality in AdS/CFT and Lovelock theory, JHEP 06 (2010) 099 [arXiv:0912.1944] [INSPIRE].
M.H. Dehghani and R. Pourhasan, Thermodynamic instability of black holes of third order Lovelock gravity, Phys. Rev. D 79 (2009) 064015 [arXiv:0903.4260] [INSPIRE].
A. Belin, A. Maloney and S. Matsuura, Holographic Phases of Renyi Entropies, JHEP 12 (2013) 050 [arXiv:1306.2640] [INSPIRE].
A. Belin, L.-Y. Hung, A. Maloney and S. Matsuura, Charged Renyi entropies and holographic superconductors, JHEP 01 (2015) 059 [arXiv:1407.5630] [INSPIRE].
E. Witten, Conformal Field Theory In Four And Six Dimensions, arXiv:0712.0157 [INSPIRE].
J.C. Baez, Renyi entropy and free energy, arXiv:1102.2098.
S.W. Hawking, Gravitational radiation from colliding black holes, Phys. Rev. Lett. 26 (1971) 1344 [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4 (1972) 737 [INSPIRE].
J.D. Bekenstein, Generalized second law of thermodynamics in black hole physics, Phys. Rev. D 9 (1974) 3292 [INSPIRE].
S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [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].
T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D 49 (1994) 6587 [gr-qc/9312023] [INSPIRE].
A. Yale, Simple counterterms for asymptotically AdS spacetimes in Lovelock gravity, Phys. Rev. D 84 (2011) 104036 [arXiv:1107.1250] [INSPIRE].
M.R. Mehdizadeh, M.H. Dehghani and M.K. Zangeneh, Counterterms for Static Lovelock Solutions, Eur. Phys. J. C 75 (2015) 276 [arXiv:1501.05218] [INSPIRE].
M.H. Dehghani, N. Bostani and A. Sheykhi, Counterterm method in Lovelock theory and horizonless solutions in dimensionally continued gravity, Phys. Rev. D 73 (2006) 104013 [hep-th/0603058] [INSPIRE].
D. Astefanesei, N. Banerjee and S. Dutta, (Un)attractor black holes in higher derivative AdS gravity, JHEP 11 (2008) 070 [arXiv:0806.1334] [INSPIRE].
M. Cvetič, S. Nojiri and S.D. Odintsov, Black hole thermodynamics and negative entropy in de Sitter and anti-de Sitter Einstein-Gauss-Bonnet gravity, Nucl. Phys. B 628 (2002) 295 [hep-th/0112045] [INSPIRE].
G. Kofinas and R. Olea, Universal regularization prescription for Lovelock AdS gravity, JHEP 11 (2007) 069 [arXiv:0708.0782] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [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].
L. Vanzo, Black holes with unusual topology, Phys. Rev. D 56 (1997) 6475 [gr-qc/9705004] [INSPIRE].
P. Kraus, F. Larsen and R. Siebelink, The gravitational action in asymptotically AdS and flat space-times, Nucl. Phys. B 563 (1999) 259 [hep-th/9906127] [INSPIRE].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, The Viscosity Bound and Causality Violation, Phys. Rev. Lett. 100 (2008) 191601 [arXiv:0802.3318] [INSPIRE].
A. Buchel and R.C. Myers, Causality of Holographic Hydrodynamics, JHEP 08 (2009) 016 [arXiv:0906.2922] [INSPIRE].
A. Buchel, J. Escobedo, R.C. Myers, M.F. Paulos, A. Sinha and M. Smolkin, Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].
X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007 [arXiv:0911.3160] [INSPIRE].
D.M. Hofman, Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT, Nucl. Phys. B 823 (2009) 174 [arXiv:0907.1625] [INSPIRE].
J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Lovelock Gravities and Black Holes, JHEP 06 (2010) 008 [arXiv:0912.1877] [INSPIRE].
G. Pastras and D. Manolopoulos, Charged Rényi entropies in CFTs with Einstein-Gauss-Bonnet holographic duals, JHEP 11 (2014) 007 [arXiv:1404.1309] [INSPIRE].
G. Pastras and D. Manolopoulos, Holographic Calculation of Renyi Entropies and Restrictions on Higher Derivative Terms, PoS (CORFU2014) 157 [arXiv:1507.08595] [INSPIRE].
M.A. Metlitski, C.A. Fuertes and S. Sachdev, Entanglement Entropy in the O(N) model, Phys. Rev. B 80 (2009) 115122 [arXiv:0904.4477] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N ) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
E. Sezgin and P. Sundell, Holography in 4D (super) higher spin theories and a test via cubic scalar couplings, JHEP 07 (2005) 044 [hep-th/0305040] [INSPIRE].
S. Giombi, Tasi lectures on higher Spin-CFT duality, arXiv:1607.02967 [INSPIRE].
J.-M. Stéphan, G. Misguich and V. Pasquier, Phase transition in the Rényi-Shannon entropy of luttinger liquids, Phys. Rev. B 84 (2011) 195128 [arXiv:1104.2544].
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: 1704.08731
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
Puletti, V.G.M., Pourhasan, R. Non-analyticity of holographic Rényi entropy in Lovelock gravity. J. High Energ. Phys. 2017, 2 (2017). https://doi.org/10.1007/JHEP08(2017)002
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2017)002