Abstract
Gauge/gravity duality relates an AdS black hole with uniform boost with a boosted strongly-coupled CFT at finite temperature. We study the perturbative change in holographic entanglement entropy for strip sub-region in such gravity solutions up to third order and try to formulate a first law of entanglement thermodynamics including higher order corrections. The first law receives important contribution from an entanglement chemical potential in presence of boost. We find that suitable modifications to the entanglement temperature and entanglement chemical potential are required to account for higher order corrections. The results can be extended to non-conformal cases and AdS plane wave background.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [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].
M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [arXiv:1005.3035] [INSPIRE].
J. Bhattacharya, M. Nozaki, T. Takayanagi and T. Ugajin, Thermodynamical Property of Entanglement Entropy for Excited States, Phys. Rev. Lett. 110 (2013) 091602 [arXiv:1212.1164] [INSPIRE].
D. Allahbakhshi, M. Alishahiha and A. Naseh, Entanglement Thermodynamics, JHEP 08 (2013) 102 [arXiv:1305.2728] [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].
G. Wong, I. Klich, L.A. Pando Zayas and D. Vaman, Entanglement Temperature and Entanglement Entropy of Excited States, JHEP 12 (2013) 020 [arXiv:1305.3291] [INSPIRE].
D.-W. Pang, Entanglement thermodynamics for nonconformal D-branes, Phys. Rev. D 88 (2013) 126001 [arXiv:1310.3676] [INSPIRE].
S. He, J.-R. Sun and H.-Q. Zhang, On Holographic Entanglement Entropy with Second Order Excitations, Nucl. Phys. B 928 (2018) 160 [arXiv:1411.6213] [INSPIRE].
S. Chakraborty, P. Dey, S. Karar and S. Roy, Entanglement thermodynamics for an excited state of Lifshitz system, JHEP 04 (2015) 133 [arXiv:1412.1276] [INSPIRE].
R. Mishra and H. Singh, Perturbative entanglement thermodynamics for AdS spacetime: Renormalization, JHEP 10 (2015) 129 [arXiv:1507.03836] [INSPIRE].
A. Ghosh and R. Mishra, Generalized geodesic deviation equations and an entanglement first law for rotating BTZ black holes, Phys. Rev. D 94 (2016) 126005 [arXiv:1607.01178] [INSPIRE].
A. Bhattacharya and S. Roy, Holographic entanglement entropy and entanglement thermodynamics of ‘black’ non-SUSY D3 brane, Phys. Lett. B 781 (2018) 232 [arXiv:1712.03740] [INSPIRE].
S. F. Lokhande, G. W. J. Oling and J. F. Pedraza, Linear response of entanglement entropy from holography, JHEP 10 (2017) 104 [arXiv:1705.10324] [INSPIRE].
S. Maulik and H. Singh, Holographic entanglement entropy for \( {Lif}_4^{(2)} \) × S1 × S5 spacetime with string excitations, Phys. Rev. D 103 (2021) 066003 [arXiv:1911.10865] [INSPIRE].
M. Fujita, S. He and Y. Sun, Thermodynamical property of entanglement entropy and deconfinement phase transition, Phys. Rev. D 102 (2020) 126019 [arXiv:2005.01048] [INSPIRE].
N. Lashkari, M. B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement ‘thermodynamics’, JHEP 04 (2014) 195 [arXiv:1308.3716] [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].
B. Swingle and M. Van Raamsdonk, Universality of Gravity from Entanglement, arXiv:1405.2933 [INSPIRE].
T. Faulkner, F. M. Haehl, E. Hijano, O. Parrikar, C. Rabideau and M. Van Raamsdonk, Nonlinear Gravity from Entanglement in Conformal Field Theories, JHEP 08 (2017) 057 [arXiv:1705.03026] [INSPIRE].
K.-S. Kim and C. Park, Renormalization group flow of entanglement entropy to thermal entropy, Phys. Rev. D 95 (2017) 106007 [arXiv:1610.07266] [INSPIRE].
A. Saha, S. Gangopadhyay and J. P. Saha, Holographic entanglement entropy and generalized entanglement temperature, Phys. Rev. D 100 (2019) 106008 [arXiv:1906.03159] [INSPIRE].
J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [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. Bianchi, D. Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
H. Singh, Special limits and non-relativistic solutions, JHEP 12 (2010) 061 [arXiv:1009.0651] [INSPIRE].
H. Singh, Lifshitz/Schrödinger Dp-branes and dynamical exponents, JHEP 07 (2012) 082 [arXiv:1202.6533] [INSPIRE].
K. Narayan, T. Takayanagi and S. P. Trivedi, AdS plane waves and entanglement entropy, JHEP 04 (2013) 051 [arXiv:1212.4328] [INSPIRE].
D. Mukherjee and K. Narayan, AdS plane waves, entanglement and mutual information, Phys. Rev. D 90 (2014) 026003 [arXiv:1405.3553] [INSPIRE].
R. Mishra and H. Singh, Entanglement asymmetry for boosted black branes and the bound, Int. J. Mod. Phys. A 32 (2017) 1750091 [arXiv:1603.06058] [INSPIRE].
N. Itzhaki, J. M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
A. Lala, Entanglement measures for nonconformal D-branes, Phys. Rev. D 102 (2020) 126026 [arXiv:2008.06154] [INSPIRE].
J. R. Garrison and T. Grover, Does a single eigenstate encode the full Hamiltonian?, Phys. Rev. X 8 (2018) 021026 [arXiv:1503.00729] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2012.09530
Rights and permissions
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.
About this article
Cite this article
Maulik, S., Singh, H. Entanglement entropy and the first law at third order for boosted black branes. J. High Energ. Phys. 2021, 65 (2021). https://doi.org/10.1007/JHEP04(2021)065
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)065