Abstract
We derive the geodesic equation for determining the Ryu-Takayanagi surface in AdS3 deformed by single trace \( \mu T\overline{T} \) + \( {\varepsilon}_{+}J\overline{T} \) + \( {\varepsilon}_{-}T\overline{J} \) deformation for generic values of (μ, ε+, ε−) for which the background is free of singularities. For generic values of ε±, Lorentz invariance is broken, and the Ryu-Takayanagi surface embeds non-trivially in time as well as spatial coordinates. We solve the geodesic equation and characterize the UV and IR behavior of the entanglement entropy and the Casini-Huerta c-function. We comment on various features of these observables in the (μ, ε+, ε−) parameter space. We discuss the matching at leading order in small (μ, ε+, ε−) expansion of the entanglement entropy between the single trace deformed holographic system and a class of double trace deformed theories where a strictly field theoretic analysis is possible. We also comment on expectation value of a large rectangular Wilson loop-like observable.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Chakraborty, A. Giveon and D. Kutasov, \( T\overline{T} \), \( J\overline{T} \), \( T\overline{J} \) and String Theory, J. Phys. A 52 (2019) 384003 [arXiv:1905.00051] [INSPIRE].
L. Apolo and W. Song, Heating up holography for single-trace \( J\overline{T} \) deformations, JHEP 01 (2020) 141 [arXiv:1907.03745] [INSPIRE].
L. Apolo, S. Detournay and W. Song, TsT, \( T\overline{T} \) and black strings, JHEP 06 (2020) 109 [arXiv:1911.12359] [INSPIRE].
S. Chakraborty and A. Hashimoto, Thermodynamics of \( T\overline{T} \), \( J\overline{T} \), \( T\overline{J} \) deformed conformal field theories, JHEP 07 (2020) 188 [arXiv:2006.10271] [INSPIRE].
T. Araujo, E.O. Colgáin, Y. Sakatani, M.M. Sheikh-Jabbari and H. Yavartanoo, Holographic integration of \( T\overline{T} \) & \( J\overline{T} \) via O(d, d), JHEP 03 (2019) 168 [arXiv:1811.03050] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, \( T\overline{T} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, \( J\overline{T} \) deformed CFT2 and string theory, JHEP 10 (2018) 057 [arXiv:1806.09667] [INSPIRE].
L. Apolo and W. Song, Strings on warped AdS3 via \( T\overline{J} \) deformations, JHEP 10 (2018) 165 [arXiv:1806.10127] [INSPIRE].
F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \) -deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, SciPost Phys. 5 (2018) 048 [arXiv:1710.08415] [INSPIRE].
B. Le Floch and M. Mezei, Solving a family of \( T\overline{T} \)-like theories, arXiv:1903.07606 [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, Strings in irrelevant deformations of AdS3/CFT2, JHEP 11 (2020) 057 [arXiv:2009.03929] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: An Overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].
J.L.F. Barbón and C.A. Fuertes, Holographic entanglement entropy probes (non)locality, JHEP 04 (2008) 096 [arXiv:0803.1928] [INSPIRE].
W. Fischler, A. Kundu and S. Kundu, Holographic Entanglement in a Noncommutative Gauge Theory, JHEP 01 (2014) 137 [arXiv:1307.2932] [INSPIRE].
J.L. Karczmarek and C. Rabideau, Holographic entanglement entropy in nonlocal theories, JHEP 10 (2013) 078 [arXiv:1307.3517] [INSPIRE].
S. Chakraborty, A. Giveon, N. Itzhaki and D. Kutasov, Entanglement beyond AdS, Nucl. Phys. B 935 (2018) 290 [arXiv:1805.06286] [INSPIRE].
M. Asrat and J. Kudler-Flam, \( T\overline{T} \), the entanglement wedge cross section, and the breakdown of the split property, Phys. Rev. D 102 (2020) 045009 [arXiv:2005.08972] [INSPIRE].
M. Asrat, Entropic c-functions in \( T\overline{T} \), \( J\overline{T} \), \( T\overline{J} \) deformations, Nucl. Phys. B 960 (2020) 115186 [arXiv:1911.04618] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, \( T\overline{T} \), black holes and negative strings, JHEP 09 (2020) 057 [arXiv:2006.13249] [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].
S. Chakraborty, \( \frac{\mathrm{SL}\left(2,\mathrm{\mathbb{R}}\right)\times \mathrm{U}(1)}{\mathrm{U}(1)} \) CFT, NS5 + F1 system and single trace \( T\overline{T} \), arXiv:2012.03995 [INSPIRE].
A. Hashimoto and D. Kutasov, \( T\overline{T} \), \( J\overline{T} \), \( T\overline{J} \) partition sums from string theory, JHEP 02 (2020) 080 [arXiv:1907.07221] [INSPIRE].
M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, in Lecture Notes in Physics 931, Springer, Cham Switzerland (2017) [arXiv:1609.01287] [INSPIRE].
A. Castro, D.M. Hofman and N. Iqbal, Entanglement Entropy in Warped Conformal Field Theories, JHEP 02 (2016) 033 [arXiv:1511.00707] [INSPIRE].
W. Song, Q. Wen and J. Xu, Modifications to Holographic Entanglement Entropy in Warped CFT, JHEP 02 (2017) 067 [arXiv:1610.00727] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
A. Lewkowycz, J. Liu, E. Silverstein and G. Torroba, \( T\overline{T} \) and EE, with implications for (A)dS subregion encodings, JHEP 04 (2020) 152 [arXiv:1909.13808] [INSPIRE].
Y. Sun and J.-R. Sun, Note on the Rényi entropy of 2D perturbed fermions, Phys. Rev. D 99 (2019) 106008 [arXiv:1901.08796] [INSPIRE].
S. He and H. Shu, Correlation functions, entanglement and chaos in the \( T\overline{T}/J\overline{T} \) –deformed CFTs, JHEP 02 (2020) 088 [arXiv:1907.12603] [INSPIRE].
X. Dong, The Gravity Dual of Renyi Entropy, Nature Commun. 7 (2016) 12472 [arXiv:1601.06788] [INSPIRE].
V. Rosenhaus and M. Smolkin, Entanglement Entropy for Relevant and Geometric Perturbations, JHEP 02 (2015) 015 [arXiv:1410.6530] [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. Kutasov, Geometry on the Space of Conformal Field Theories and Contact Terms, Phys. Lett. B 220 (1989) 153 [INSPIRE].
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S. Chakraborty, Wilson loop in a \( T\overline{T} \) like deformed CFT2, Nucl. Phys. B 938 (2019) 605 [arXiv:1809.01915] [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: 2010.15759
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
Chakraborty, S., Hashimoto, A. Entanglement entropy for \( \mathrm{T}\overline{\mathrm{T}} \), \( \mathrm{J}\overline{\mathrm{T}} \), \( \mathrm{T}\overline{\mathrm{J}} \) deformed holographic CFT. J. High Energ. Phys. 2021, 96 (2021). https://doi.org/10.1007/JHEP02(2021)096
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2021)096