Holographic entanglement entropy in Lovelock gravities. (English) Zbl 1298.81265
Summary: We study entanglement entropies of simply connected surfaces in field theories dual to Lovelock gravities. We consider Gauss-Bonnet and cubic Lovelock gravities in detail. In the conformal case the logarithmic terms in the entanglement entropy are governed by the conformal anomalies of the CFT; we verify that the holographic calculations are consistent with this property. We also compute the holographic entanglement entropy of a slab in the Gauss-Bonnet examples dual to relativistic and non-relativistic CFTs and discuss its properties. Finally, we discuss features of the entanglement entropy in the backgrounds dual to renormalization group flows between fixed points and comment on the implications for a possible c-theorem in four spacetime dimensions.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81V17 | Gravitational interaction in quantum theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T50 | Anomalies in quantum field theory |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 94A17 | Measures of information, entropy |
References:
| [1] | S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001] [SPIRES]. · Zbl 1228.83110 · doi:10.1103/PhysRevLett.96.181602 |
| [2] | S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP08 (2006) 045 [hep-th/0605073] [SPIRES]. · doi:10.1088/1126-6708/2006/08/045 |
| [3] | D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP05 (2008) 012 [arXiv:0803.1467] [SPIRES]. · doi:10.1088/1126-6708/2008/05/012 |
| [4] | A.B. Zamolodchikov, Irreversibility of the flux of the renormalization group in a 2D field theory, JETP Lett.43 (1986) 730 [Pisma Zh. Eksp. Teor. Fiz.43 (1986) 565] [SPIRES]. |
| [5] | J.L. Cardy, Is there a c theorem in four-dimensions?, Phys. Lett.B 215 (1988) 749 [SPIRES]. |
| [6] | D. Erkal and D. Kutasov, a-maximization, global symmetries and RG flows, arXiv:1007.2176 [SPIRES]. |
| [7] | D. Poland and D. Simmons-Duffin, Bounds on 4D conformal and superconformal field theories, JHEP05 (2011) 017 [arXiv:1009.2087] [SPIRES]. · Zbl 1296.81067 · doi:10.1007/JHEP05(2011)017 |
| [8] | D. Gaiotto, N. Seiberg and Y. Tachikawa, Comments on scaling limits of 4D N = 2 theories, JHEP01 (2011) 078 [arXiv:1011.4568] [SPIRES]. · Zbl 1214.81154 · doi:10.1007/JHEP01(2011)078 |
| [9] | R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev.D 82 (2010) 046006 [arXiv:1006.1263] [SPIRES]. |
| [10] | R.C. Myers and A. Sinha, Holographic c-theorems in arbitrary dimensions, JHEP01 (2011) 125 [arXiv:1011.5819] [SPIRES]. · Zbl 1214.83036 · doi:10.1007/JHEP01(2011)125 |
| [11] | J.T. Liu, W. Sabra and Z. Zhao, Holographic c-theorems and higher derivative gravity, arXiv:1012.3382 [SPIRES]. |
| [12] | 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] [SPIRES]. |
| [13] | 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] [SPIRES]. · doi:10.1103/PhysRevLett.100.191601 |
| [14] | A. Buchel and R.C. Myers, Causality of holographic hydrodynamics, JHEP08 (2009) 016 [arXiv:0906.2922] [SPIRES]. · doi:10.1088/1126-6708/2009/08/016 |
| [15] | 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] [SPIRES]. · Zbl 1196.81266 · doi:10.1016/j.nuclphysb.2009.08.001 |
| [16] | J. de Boer, M. Kulaxizi and A. Parnachev, AdS7/CFT6, Gauss-Bonnet gravity and viscosity bound, JHEP03 (2010) 087 [arXiv:0910.5347] [SPIRES]. · Zbl 1271.83048 · doi:10.1007/JHEP03(2010)087 |
| [17] | X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP04 (2010) 007 [arXiv:0911.3160] [SPIRES]. · Zbl 1272.83044 · doi:10.1007/JHEP04(2010)007 |
| [18] | A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP03 (2010) 111 [arXiv:0911.4257] [SPIRES]. · Zbl 1271.81120 · doi:10.1007/JHEP03(2010)111 |
| [19] | J.deBoer, M. Kulaxizi and A. Parnachev, Holographic Lovelock gravities and black holes, JHEP06 (2010) 008 [arXiv:0912.1877] [SPIRES]. · Zbl 1290.81112 · doi:10.1007/JHEP06(2010)008 |
| [20] | X.O. Camanho and J.D. Edelstein, Causality in AdS/CFT and Lovelock theory, JHEP06 (2010) 099 [arXiv:0912.1944] [SPIRES]. · Zbl 1288.83018 · doi:10.1007/JHEP06(2010)099 |
| [21] | R.C. Myers, M.F. Paulos and A. Sinha, Holographic studies of quasi-topological gravity, JHEP08 (2010) 035 [arXiv:1004.2055] [SPIRES]. · Zbl 1291.83156 · doi:10.1007/JHEP08(2010)035 |
| [22] | M. Kulaxizi and A. Parnachev, Energy flux positivity and unitarity in CFTs, Phys. Rev. Lett.106 (2011) 011601 [arXiv:1007.0553] [SPIRES]. · doi:10.1103/PhysRevLett.106.011601 |
| [23] | A. Buchel and S. Cremonini, Viscosity bound and causality in superfluid plasma, JHEP10 (2010) 026 [arXiv:1007.2963] [SPIRES]. · Zbl 1291.76367 · doi:10.1007/JHEP10(2010)026 |
| [24] | R.C. Myers, S. Sachdev and A. Singh, Holographic quantum critical transport without self-duality, Phys. Rev.D 83 (2011) 066017 [arXiv:1010.0443] [SPIRES]. |
| [25] | X.O. Camanho, J.D. Edelstein and M.F. Paulos, Lovelock theories, holography and the fate of the viscosity bound, JHEP05 (2011) 127 [arXiv:1010.1682] [SPIRES]. · Zbl 1296.83009 · doi:10.1007/JHEP05(2011)127 |
| [26] | S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett.B 665 (2008) 305 [arXiv:0802.3117] [SPIRES]. · Zbl 1328.81209 |
| [27] | D.V. Fursaev, Proof of the holographic formula for entanglement entropy, JHEP09 (2006) 018 [hep-th/0606184] [SPIRES]. · doi:10.1088/1126-6708/2006/09/018 |
| [28] | L.-Y. Hung, R.C. Myers and M. Smolkin, On holographic entanglement entropy and higher curvature gravity, JHEP04 (2011) 025 [arXiv:1101.5813] [SPIRES]. · doi:10.1007/JHEP04(2011)025 |
| [29] | H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP05 (2011) 036 [arXiv:1102.0440] [SPIRES]. · Zbl 1296.81073 · doi:10.1007/JHEP05(2011)036 |
| [30] | L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin, A quantum source of entropy for black holes, Phys. Rev.D 34 (1986) 373 [SPIRES]. · Zbl 1222.83077 |
| [31] | M. Srednicki, Entropy and area, Phys. Rev. Lett.71 (1993) 666 [hep-th/9303048] [SPIRES]. · Zbl 0972.81649 · doi:10.1103/PhysRevLett.71.666 |
| [32] | M.B. Plenio, J. Eisert, J. Dreissig and M. Cramer, Entropy, entanglement and area: analytical results for harmonic lattice systems, Phys. Rev. Lett.94 (2005) 060503 [quant-ph/0405142] [SPIRES]. · doi:10.1103/PhysRevLett.94.060503 |
| [33] | M. Cramer, J. Eisert, M.B. Plenio and J. Dreissig, An entanglement-area law for general bosonic harmonic lattice systems, Phys. Rev.A 73 (2006) 012309 [quant-ph/0505092] [SPIRES]. |
| [34] | M. Ahmadi, S. Das and S. Shankaranarayanan, Is entanglement entropy proportional to area?, Can. J. Phys.84 (2006) 493 [hep-th/0507228] [SPIRES]. · doi:10.1139/p06-002 |
| [35] | S. Das and S. Shankaranarayanan, How robust is the entanglement entropy-area relation?, Phys. Rev.D 73 (2006) 121701 [gr-qc/0511066] [SPIRES]. |
| [36] | H. Casini, Geometric entropy, area and strong subadditivity, Class. Quant. Grav.21 (2004) 2351 [hep-th/0312238] [SPIRES]. · Zbl 1055.83020 · doi:10.1088/0264-9381/21/9/011 |
| [37] | H. Casini and M. Huerta, Analytic results on the geometric entropy for free fields, J. Stat. Mech. (2008) P01012 [arXiv:0707.1300] [SPIRES]. · Zbl 1456.81301 |
| [38] | M.M. Wolf, Violation of the entropic area law for fermions, Phys. Rev. Lett.96 (2004) 010404 [quant-ph/0503219]. · doi:10.1103/PhysRevLett.96.010404 |
| [39] | D. Gioev and I. Klich, Entanglement entropy of fermions in any dimension and the Widom conjecture, Phys. Rev. Lett.96 (2006) 100503 [quant-ph/0504151]. · doi:10.1103/PhysRevLett.96.100503 |
| [40] | T. Barthel, M. Chung and U. Schollwoeck, Entanglement scaling in critical two-dimensional fermionic and bosonic systems, Phys. Rev.A 74 (2006) 022329 [cond-mat/0602077]. |
| [41] | W. Li, L. Leitian Ding, R. Yu, T. Roscilde and S. Haas, Scaling behavior of entanglement in two-and three-dimensional free fermions, Phys. Rev.B 74 (2007) 0703103 [quant-ph/0602094]. |
| [42] | H. Casini and M. Huerta, Universal terms for the entanglement entropy in 2 + 1 dimensions, Nucl. Phys.B 764 (2007) 183 [hep-th/0606256] [SPIRES]. · Zbl 1116.81008 · doi:10.1016/j.nuclphysb.2006.12.012 |
| [43] | R. Lohmayer, H. Neuberger, A. Schwimmer and S. Theisen, Numerical determination of entanglement entropy for a sphere, Phys. Lett.B 685 (2010) 222 [arXiv:0911.4283] [SPIRES]. |
| [44] | H. Casini and M. Huerta, Entanglement entropy for the n-sphere, Phys. Lett.B 694 (2010) 167 [arXiv:1007.1813] [SPIRES]. |
| [45] | J.S. Dowker, Hyperspherical entanglement entropy, J. Phys.A 43 (2010) 445402 [arXiv:1007.3865] [SPIRES]. · Zbl 1209.81030 |
| [46] | J.S. Dowker, Entanglement entropy for even spheres, arXiv:1009.3854 [SPIRES]. |
| [47] | J.S. Dowker, Determinants and conformal anomalies of GJMS operators on spheres, J. Phys.A 44 (2011) 115402 [arXiv:1010.0566] [SPIRES]. · Zbl 1210.81099 |
| [48] | J.S. Dowker, Entanglement entropy for odd spheres, arXiv:1012.1548 [SPIRES]. |
| [49] | Q. Exirifard and M.M. Sheikh-Jabbari, Lovelock gravity at the crossroads of Palatini and metric formulations, Phys. Lett.B 661 (2008) 158 [arXiv:0705.1879] [SPIRES]. · Zbl 1246.83167 |
| [50] | D.G. Boulware and S. Deser, String generated gravity models, Phys. Rev. Lett.55 (1985) 2656 [SPIRES]. · doi:10.1103/PhysRevLett.55.2656 |
| [51] | R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev.D 65 (2002) 084014 [hep-th/0109133] [SPIRES]. |
| [52] | M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP07 (1998) 023 [hep-th/9806087] [SPIRES]. · Zbl 0958.81083 · doi:10.1088/1126-6708/1998/07/023 |
| [53] | M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys.48 (2000) 125 [hep-th/9812032] [SPIRES]. · Zbl 0976.81093 · doi:10.1002/(SICI)1521-3978(20001)48:1/3<125::AID-PROP125>3.0.CO;2-B |
| [54] | S. Nojiri and S.D. Odintsov, On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence, Int. J. Mod. Phys.A 15 (2000) 413 [hep-th/9903033] [SPIRES]. · Zbl 0952.81053 |
| [55] | V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP07 (2007) 062 [arXiv:0705.0016] [SPIRES]. · doi:10.1088/1126-6708/2007/07/062 |
| [56] | T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: an overview, J. Phys.A 42 (2009) 504008 [arXiv:0905.0932] [SPIRES]. · Zbl 1179.81138 |
| [57] | M. Headrick and T. Takayanagi, A holographic proof of the strong subadditivity of entanglement entropy, Phys. Rev.D 76 (2007) 106013 [arXiv:0704.3719] [SPIRES]. |
| [58] | C. Holzhey, F. Larsen and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys.B 424 (1994) 443 [hep-th/9403108] [SPIRES]. · Zbl 0990.81564 · doi:10.1016/0550-3213(94)90402-2 |
| [59] | P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004) P06002 [hep-th/0405152] [SPIRES]. · Zbl 1082.82002 |
| [60] | 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] [SPIRES]. · Zbl 1097.81014 · doi:10.1142/S021974990600192X |
| [61] | J.-R. Sun, Note on Chern-Simons term correction to holographic entanglement entropy, JHEP05 (2009) 061 [arXiv:0810.0967] [SPIRES]. · doi:10.1088/1126-6708/2009/05/061 |
| [62] | 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] [SPIRES]. |
| [63] | D.V. Fursaev and S.N. Solodukhin, On one loop renormalization of black hole entropy, Phys. Lett.B 365 (1996) 51 [hep-th/9412020] [SPIRES]. |
| [64] | S.N. Solodukhin, On ’non-geometric’ contribution to the entropy of black hole due to quantum corrections, Phys. Rev.D 51 (1995) 618 [hep-th/9408068] [SPIRES]. |
| [65] | S.N. Solodukhin, The conical singularity and quantum corrections to entropy of black hole, Phys. Rev.D 51 (1995) 609 [hep-th/9407001] [SPIRES]. |
| [66] | D.V. Fursaev, Black hole thermodynamics and renormalization, Mod. Phys. Lett.A 10 (1995) 649 [hep-th/9408066] [SPIRES]. · Zbl 1020.83600 |
| [67] | D.V. Fursaev, Spectral geometry and one loop divergences on manifolds with conical singularities, Phys. Lett.B 334 (1994) 53 [hep-th/9405143] [SPIRES]. |
| [68] | D. Nesterov and S.N. Solodukhin, Short-distance regularity of Green’s function and UV divergences in entanglement entropy, JHEP09 (2010) 041 [arXiv:1008.0777] [SPIRES]. · Zbl 1291.81218 · doi:10.1007/JHEP09(2010)041 |
| [69] | T. Padmanabhan, Finite entanglement entropy from the zero-point-area of spacetime, Phys. Rev.D 82 (2010) 124025 [arXiv:1007.5066] [SPIRES]. |
| [70] | D. Nesterov and S.N. Solodukhin, Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry, Nucl. Phys.B 842 (2011) 141 [arXiv:1007.1246] [SPIRES]. · Zbl 1207.81091 · doi:10.1016/j.nuclphysb.2010.08.006 |
| [71] | M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev.D 82 (2010) 126010 [arXiv:1006.0047] [SPIRES]. |
| [72] | T. Jacobson and R.C. Myers, Black hole entropy and higher curvature interactions, Phys. Rev. Lett.70 (1993) 3684 [hep-th/9305016] [SPIRES]. · Zbl 1050.83508 · doi:10.1103/PhysRevLett.70.3684 |
| [73] | M. Bañados, C. Teitelboim and J. Zanelli, Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem, Phys. Rev. Lett.72 (1994) 957 [gr-qc/9309026] [SPIRES]. · Zbl 0973.83531 · doi:10.1103/PhysRevLett.72.957 |
| [74] | W. Nelson, A comment on black hole entropy in string theory, Phys. Rev.D 50 (1994) 7400 [hep-th/9406011] [SPIRES]. |
| [75] | V. Iyer and R.M. Wald, A comparison of Noether charge and euclidean methods for computing the entropy of stationary black holes, Phys. Rev.D 52 (1995) 4430 [gr-qc/9503052] [SPIRES]. |
| [76] | I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys.B 796 (2008) 274 [arXiv:0709.2140] [SPIRES]. · Zbl 1219.81214 · doi:10.1016/j.nuclphysb.2007.12.017 |
| [77] | M. Kulaxizi and A. Parnachev, Supersymmetry constraints in holographic gravities, Phys. Rev.D 82 (2010) 066001 [arXiv:0912.4244] [SPIRES]. |
| [78] | S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev.D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES]. |
| [79] | K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP08 (2010) 014 [arXiv:1005.3291] [SPIRES]. · Zbl 1291.83195 · doi:10.1007/JHEP08(2010)014 |
| [80] | A. Donos and J.P. Gauntlett, Lifshitz solutions of D = 10 and D = 11 supergravity, JHEP12 (2010) 002 [arXiv:1008.2062] [SPIRES]. · Zbl 1294.81099 · doi:10.1007/JHEP12(2010)002 |
| [81] | A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP12 (2010) 003 [arXiv:1009.3805] [SPIRES]. · Zbl 1294.81192 · doi:10.1007/JHEP12(2010)003 |
| [82] | R. Gregory, S.L. Parameswaran, G. Tasinato and I. Zavala, Lifshitz solutions in supergravity and string theory, JHEP12 (2010) 047 [arXiv:1009.3445] [SPIRES]. · Zbl 1294.81198 · doi:10.1007/JHEP12(2010)047 |
| [83] | A. Adams, A. Maloney, A. Sinha and S.E. Vazquez, 1/N effects in non-relativistic gauge-gravity duality, JHEP03 (2009) 097 [arXiv:0812.0166] [SPIRES]. · doi:10.1088/1126-6708/2009/03/097 |
| [84] | M.H. Dehghani and R.B. Mann, Lovelock-Lifshitz black holes, JHEP07 (2010) 019 [arXiv:1004.4397] [SPIRES]. · Zbl 1290.83037 · doi:10.1007/JHEP07(2010)019 |
| [85] | M.H. Dehghani and R.B. Mann, Thermodynamics of Lovelock-Lifshitz black branes, Phys. Rev.D 82 (2010) 064019 [arXiv:1006.3510] [SPIRES]. |
| [86] | A.H. Chamseddine, Topological gauge theory of gravity in five-dimensions and all odd dimensions, Phys. Lett.B 233 (1989) 291 [SPIRES]. · Zbl 1332.81131 |
| [87] | S.N. Solodukhin, Entanglement entropy in non-relativistic field theories, JHEP04 (2010) 101 [arXiv:0909.0277] [SPIRES]. · Zbl 1272.81023 · doi:10.1007/JHEP04(2010)101 |
| [88] | T. Azeyanagi, W. Li and T. Takayanagi, On string theory duals of Lifshitz-like fixed points, JHEP06 (2009) 084 [arXiv:0905.0688] [SPIRES]. · doi:10.1088/1126-6708/2009/06/084 |
| [89] | C. Hoyos and P. Koroteev, On the null energy condition and causality in Lifshitz holography, Phys. Rev.D 82 (2010) 084002 [Erratum ibid.D 82 (2010) 109905] [arXiv:1007.1428] [SPIRES]. |
| [90] | M. Berg and H. Samtleben, An exact holographic RG flow between 2D conformal fixed points, JHEP05 (2002) 006 [hep-th/0112154] [SPIRES]. · doi:10.1088/1126-6708/2002/05/006 |
| [91] | M. Taylor, More on counterterms in the gravitational action and anomalies, hep-th/0002125 [SPIRES]. |
| [92] | M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys.B 631 (2002) 159 [hep-th/0112119] [SPIRES]. · Zbl 0995.81075 |
| [93] | I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, hep-th/0404176 [SPIRES]. · Zbl 1081.81085 |
| [94] | H. Casini and M. Huerta, A finite entanglement entropy and the c-theorem, Phys. Lett.B 600 (2004) 142 [hep-th/0405111] [SPIRES]. · Zbl 1247.81021 |
| [95] | H. Casini and M. Huerta, A c-theorem for the entanglement entropy, J. Phys.A 40 (2007) 7031 [cond-mat/0610375] [SPIRES]. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
