Entanglement entropy in Horndeski gravity

Document Type : Regular article

Author

Instituto de Física, Universidade Federal do Rio de Janeiro, Brazil.

Abstract

In this work, we explore the holographic entanglement entropy with an infinite strip region of the boundary in Horndeski gravity. In our prescription we consider the spherically and planar topologies black holes in the AdS$_{4}$/CFT$_{3}$ scenario. In such framework, we show the behavior of the entanglement entropy in function of the Horndeski parameters. Such parameters modify the information store of subsystem A, especially when the parameter $gamma$ increases the information about the subsystem will also increase or decrease when it decreases. Thus, with this scheme we compute the “first law of entanglement thermodynamics” in Horndeski gravity and we show that a very small subsystem obeys the analogous property of the first law of thermodynamics if we excite the system.

Keywords

Main Subjects

[1] T. Takayanagi, ”Entanglement Entropy from a Holographic Viewpoint”, Class. Quant. Grav. 29 (2012), 153001, [arXiv:1204.2450 [gr-qc]].
[2] A. Bhattacharya, K. T. Grosvenor and S. Roy, ”Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime”, Phys. Rev. D 100, no.12, 126004 (2019), arXiv:1905.02220 [hep-th]].
[3] A. Bhattacharya and S. Roy, ”Holographic entanglement entropy and entanglement thermodynamics of ‘black’ non-susy D3 brane”, Phys. Lett. B 781, 232-237 (2018), [arXiv:1712.03740 [hep-th]].
[4] J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, ”Thermodynamical Property of Entanglement Entropy for Excited States”, Phys. Rev. Lett. 110, no.9, 091602 (2013), [arXiv:1212.1164 [hep-th]].
[5] P. Calabrese and J. L. Cardy, ”Entanglement entropy and quantum field theory”, J. Stat. Mech. 0406 (2004), P06002, [arXiv:hep-th/0405152 [hep-th]].
[6] C. Holzhey, F. Larsen and F. Wilczek, ”Geometric and renormalized entropy in conformal field theory”, Nucl. Phys. B 424, 443-467 (1994), [arXiv:hep-th/9403108 [hep-th]].
[7] S. Ryu and T. Takayanagi, ”Aspects of Holographic Entanglement Entropy”, JHEP 08 (2006), 045, [arXiv:hep-th/0605073 [hep-th]].
[8] S. Ryu and T. Takayanagi, ”Holographic derivation of entanglement entropy from AdS/CFT”, Phys. Rev. Lett. 96 (2006), 181602, [arXiv:hep-th/0603001 [hep-th]].
[9] L. Susskind and J. Uglum, ”Black hole entropy in canonical quantum gravity and superstring theory”, Phys. Rev. D 50 (1994), 2700-2711, [arXiv:hep-th/9401070 [hep-th]].
[10] P. Chaturvedi, V. Malvimat and G. Sengupta, ”Entanglement thermodynamics for charged black holes”, Phys. Rev. D 94, no.6, 066004 (2016), [arXiv:1601.00303 [hep- th]].
[11] E. Tonni, ”Holographic entanglement entropy: near horizon geometry and disconnected regions”, JHEP 05 (2011), 004, [arXiv:1011.0166 [hep-th]].
[12] S. A. H. Mansoori, B. Mirza, M. D. Darareh and S. Janbaz, ”Entanglement Thermodynamics of the Generalized Charged BTZ Black Hole”, Int. J. Mod. Phys. A 31 (2016) no.12, 1650067, [arXiv:1512.00096 [gr-qc]].
[13] P. Caputa, V. Jejjala and H. Soltanpanahi, ”Entanglement entropy of extremal BTZ black holes”, Phys. Rev. D 89 (2014) no.4, 046006, [arXiv:1309.7852 [hep-th]].
[14] D. D. Blanco, H. Casini, L. Y. Hung and R. C. Myers, ”Relative Entropy and Holography”, JHEP 08 (2013), 060, [arXiv:1305.3182 [hep-th]].
[15] L. Susskind, ”Entanglement and Chaos in De Sitter Holography: An SYK Example”, [arXiv:2109.14104 [hep-th]].
[16] B. S. Kay, ”Entanglement entropy and algebraic holography”, [arXiv:1605.07872 [hep-th]].
[17] C. Park, ”Holographic entanglement entropy in the nonconformal medium”, Phys. Rev. D 91 (2015) no.12, 126003, [arXiv:1501.02908 [hep-th]].
[18] S. He, J. R. Sun and H. Q. Zhang, ”On Holographic Entanglement Entropy with Second Order Excitations”, Nucl. Phys. B 928 (2018), 160-181, [arXiv:1411.6213 [hep-th]].
[19] F. F. Santos, ”Aplica¸c˜oes do Setor John da Gravidade de Horndeski nos Cen´arios de Brana Negra e Rela¸c˜ao de viscosidade/entropia, Mundo Brana e Cosmologia (In Portuguese)”, [arXiv:2006.06550 [hep-th]].
[20] F. A. Brito and F. F. Santos, ”Black brane in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity”, EPL 129, no.5, 50003 (2020), [arXiv:1901.06770 [hep-th]].
[21] F. F. Santos, E. F. Capossoli and H. Boschi-Filho, ”AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity”, Phys. Rev. D 104, no.6, 066014 (2021), [arXiv:2105.03802 [hep-th]].
[22] W. J. Jiang, H. S. Liu, H. Lu and C. N. Pope, ”DC Conductivities with Momentum Dissipation in Horndeski Theories”, JHEP 1707, 084 (2017), [arXiv:1703.00922 [hep-th]].
[23] M. Baggioli and W. J. Li, ”Diffusivities bounds and chaos in holographic Horndeski theories”, JHEP 1707, 055 (2017), [arXiv:1705.01766 [hep-th]].
[24] H. S. Liu, ”Violation of Thermal Conductivity Bound in Horndeski Theory”, Phys. Rev. D 98, no. 6, 061902 (2018), [arXiv:1804.06502 [hep-th]].
[25] Y. Z. Li and H. Lu, ”a-theorem for Horndeski gravity at the critical point”, Phys. Rev. D 97, no. 12, 126008 (2018), [arXiv:1803.08088 [hep-th]].
[26] Y. Z. Li, H. Lu and H. Y. Zhang, ”Scale Invariance vs. Conformal Invariance: Holographic Two-Point Functions in Horndeski Gravity”, Eur.Phys.J.C 79, 592 (2019), arXiv:1812.05123 [hep-th].
[27] X. H. Feng, H. S. Liu, H. L¨u and C. N. Pope, ”Black Hole Entropy and Viscosity Bound in Horndeski Gravity”, JHEP 1511, 176 (2015), [arXiv:1509.07142 [hep-th]].
[28] E. Caceres, R. Mohan and P. H. Nguyen, ”On holographic entanglement entropy of Horndeski black holes”, JHEP 10, 145 (2017), [arXiv:1707.06322 [hep-th]].
[29] K. Hajian, S. Liberati, M. M. Sheikh-Jabbari and M. H. Vahidinia, ”On Black Hole Temperature in Horndeski Gravity”, Phys. Lett. B 812, 136002 (2021), [arXiv:2005.12985 [gr-qc]].
[30] M. R. Mohammadi Mozaffar, A. Mollabashi, M. M. Sheikh-Jabbari and M. H. Vahidinia, ”Holographic Entanglement Entropy, Field Redefinition Invariance and Higher Derivative Gravity Theories”, Phys. Rev. D 94, no.4, 046002 (2016), [arXiv:1603.05713 [hep-th]].
[31] V. Balasubramanian and P. Kraus, ”A Stress tensor for Anti-de Sitter gravity”, Commun. Math. Phys. 208, 413 (1999), [hep-th/9902121].
[32] G. W. Horndeski, ”Second-order scalar-tensor field equations in a four-dimensional space”, Int. J. Theor. Phys. 10, 363 (1974).
[33] F. F. Santos, ”Rotating black hole with a probe string in Horndeski Gravity”, Eur. Phys. J. Plus 135, no.10, 810 (2020), [arXiv:2005.10983 [hep-th]].
[34] A. Cisterna and C. Erices, ”Asymptotically locally AdS and flat black holes in the presence of an electric field in the Horndeski scenario”, Phys. Rev. D 89, 084038 (2014), [arXiv:gr-qc/1401.4479].
[35] M. Bravo-Gaete and M. Hassaine, ”Thermodynamics of a BTZ black hole solution with an Horndeski source”, Phys. Rev. D 90, no.2, 024008 (2014), [arXiv:1405.4935 [hep-th]].
[36] A. Anabalon, A. Cisterna and J. Oliva, ”Asymptotically locally AdS and flat black holes in Horndeski theory”, Phys. Rev. D 89, 084050 (2014), [arXiv:gr-qc/1312.3597 [gr-qc]].
[37] C. Charmousis, E. J. Copeland, A. Padilla and P. M. Saffin, ”General second order scalar-tensor theory, self tuning, and the Fab Four”, Phys. Rev. Lett. 108, 051101 (2012), [arXiv:1106.2000 [hep-th]].
[38] C. Charmousis, E. J. Copeland, A. Padilla and P. M. Saffin, ”Self-tuning and the derivation of a class of scalar-tensor theories”, Phys. Rev. D 85, 104040 (2012), [arXiv:1112.4866 [hep-th]].
[39] A. A. Starobinsky, S. V. Sushkov and M. S. Volkov, ”The screening Horndeski cosmologies”, JCAP 1606, 007 (2016), [arXiv:1604.06085 [hep-th]].
[40] J. P. Bruneton, M. Rinaldi, A. Kanfon, A. Hees, S. Schlogel and A. Fuzfa, ”Fab Four: When John and George play gravitation and cosmology”, Adv. Astron. 2012, 430694 (2012), [arXiv:1203.4446 [gr-qc]].
[41] L. Hui and A. Nicolis, ”No-Hair Theorem for the Galileon”, Phys. Rev. Lett. 110, 241104 (2013), [arXiv:1202.1296 [hep-th]].
[42] M. Bravo-Gaete and M. Hassaine, ”Lifshitz black holes with a time-dependent scalar field in a Horndeski theory”, Phys. Rev. D 89, 104028 (2014), [arXiv:1312.7736 [hep-th]].
[43] E. Babichev and C. Charmousis, ”Dressing a black hole with a time-dependent Galileon”, JHEP 1408, 106 (2014), [arXiv:1312.3204 [gr-qc]].
[44] W. Fischler and S. Kundu, ”Strongly Coupled Gauge Theories: High and Low Tem- perature Behavior of Non-local Observables”, JHEP 05, 098 (2013), [arXiv:1212.2643 [hep-th]].
[45] D. Gioev and I. Klich, ”Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture”, Phys. Rev. Lett. 96, 100503 (2006), [arXiv:quant-ph/0504151 [quant-ph]].
[46] M. M. Wolf, ”Violation of the entropic area law for Fermions”, Phys. Rev. Lett. 96, 010404 (2006), [arXiv:quant-ph/0503219 [quant-ph]].

Volume 2, Issue 2
May 2022
Pages 1-14
  • Receive Date: 11 January 2022
  • Revise Date: 09 February 2022
  • Accept Date: 23 February 2022