Abstract
We compute the leading correction to entanglement entropy in \( T\overline{T} \) deformed massive QFTs. We show that both for massive scalar and Dirac fermion, the leading order correction to the entanglement entropy of half space comes from the boundary of the entangling surface. For the case of massive scalar, the boundary term is finite while for massive fermion, it diverges logarithmically giving rise to an additional log-square divergence in the entanglement entropy.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
Y. Jiang, A pedagogical review on solvable irrelevant deformations of 2D quantum field theory, Commun. Theor. Phys. 73 (2021) 057201 [arXiv:1904.13376] [INSPIRE].
M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, SciPost Phys. 5 (2018) 048 [arXiv:1710.08415] [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].
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].
B. Le Floch and M. Mezei, Solving a family of \( T\overline{T} \)-like theories, arXiv:1903.07606 [INSPIRE].
A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \) in two-dimensional quantum field theory, hep-th/0401146 [BONN-TH-2004-02] [INSPIRE].
J. Cardy, \( T\overline{T} \) deformation of correlation functions, JHEP 12 (2019) 160 [arXiv:1907.03394] [INSPIRE].
S. Hirano and M. Shigemori, Random boundary geometry and gravity dual of \( T\overline{T} \) deformation, JHEP 11 (2020) 108 [arXiv:2003.06300] [INSPIRE].
S. Hirano, T. Nakajima and M. Shigemori, \( T\overline{T} \) deformation of stress-tensor correlators from random geometry, JHEP 04 (2021) 270 [arXiv:2012.03972] [INSPIRE].
O. Aharony and T. Vaknin, The TT* deformation at large central charge, JHEP 05 (2018) 166 [arXiv:1803.00100] [INSPIRE].
S. He, Y. Sun and Y.-X. Zhang, \( T\overline{T} \)-flow effects on torus partition functions, JHEP 09 (2021) 061 [arXiv:2011.02902] [INSPIRE].
S. He, Note on higher-point correlation functions of the \( T\overline{T} \) or \( J\overline{T} \) deformed CFTs, Sci. China Phys. Mech. Astron. 64 (2021) 291011 [arXiv:2012.06202] [INSPIRE].
V. Rosenhaus and M. Smolkin, Integrability and renormalization under \( T\overline{T} \), Phys. Rev. D 102 (2020) 065009 [arXiv:1909.02640] [INSPIRE].
A. Dey, M. Goykhman and M. Smolkin, Composite operators in \( T\overline{T} \)-deformed free QFTs, JHEP 06 (2021) 006 [arXiv:2012.15605] [INSPIRE].
A. Dey and A. Fortinsky, Perturbative renormalization of the \( T\overline{T} \)-deformed free massive Dirac fermion, JHEP 12 (2021) 200 [arXiv:2109.10525] [INSPIRE].
W. Donnelly and V. Shyam, Entanglement entropy and \( T\overline{T} \) deformation, Phys. Rev. Lett. 121 (2018) 131602 [arXiv:1806.07444] [INSPIRE].
B. Chen, L. Chen and P.-X. Hao, Entanglement entropy in \( T\overline{T} \)-deformed CFT, Phys. Rev. D 98 (2018) 086025 [arXiv:1807.08293] [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].
S. Chakraborty and A. Hashimoto, Entanglement entropy for \( T\overline{T} \), \( J\overline{T} \), \( T\overline{J} \) deformed holographic CFT, JHEP 02 (2021) 096 [arXiv:2010.15759] [INSPIRE].
M.R. Setare and S.N. Sajadi, Holographic entanglement entropy in \( T\overline{T} \)-deformed CFTs, Gen. Rel. Grav. 54 (2022) 85 [arXiv:2203.16445] [INSPIRE].
M. He and Y. Sun, Holographic entanglement entropy in \( T\overline{T} \)-deformed AdS3, arXiv:2301.04435 [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].
A. Banerjee, A. Bhattacharyya and S. Chakraborty, Entanglement entropy for TT deformed CFT in general dimensions, Nucl. Phys. B 948 (2019) 114775 [arXiv:1904.00716] [INSPIRE].
D. Kutasov, Geometry on the space of conformal field theories and contact terms, Phys. Lett. B 220 (1989) 153 [INSPIRE].
S. He, Z.-C. Liu and Y. Sun, Entanglement entropy and modular Hamiltonian of free fermion with deformations on a torus, JHEP 09 (2022) 247 [arXiv:2207.06308] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
V. Rosenhaus and M. Smolkin, Entanglement entropy: a perturbative calculation, JHEP 12 (2014) 179 [arXiv:1403.3733] [INSPIRE].
V. Rosenhaus and M. Smolkin, Entanglement entropy, planar surfaces, and spectral functions, JHEP 09 (2014) 119 [arXiv:1407.2891] [INSPIRE].
V. Rosenhaus and M. Smolkin, Entanglement entropy for relevant and geometric perturbations, JHEP 02 (2015) 015 [arXiv:1410.6530] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
A. Giveon and D. Kutasov, Supersymmetric Rényi entropy in CFT2 and AdS3, JHEP 01 (2016) 042 [arXiv:1510.08872] [INSPIRE].
H. Casini and M. Huerta, A c-theorem for the entanglement entropy, J. Phys. A 40 (2007) 7031 [cond-mat/0610375] [INSPIRE].
J. Lee, A. Lewkowycz, E. Perlmutter and B.R. Safdi, Rényi entropy, stationarity, and entanglement of the conformal scalar, JHEP 03 (2015) 075 [arXiv:1407.7816] [INSPIRE].
H. Casini, F.D. Mazzitelli and E. Testé, Area terms in entanglement entropy, Phys. Rev. D 91 (2015) 104035 [arXiv:1412.6522] [INSPIRE].
C.P. Herzog and T. Nishioka, The edge of entanglement: getting the boundary right for non-minimally coupled scalar fields, JHEP 12 (2016) 138 [arXiv:1610.02261] [INSPIRE].
M. Guica and R. Monten, \( T\overline{T} \) and the mirage of a bulk cutoff, SciPost Phys. 10 (2021) 024 [arXiv:1906.11251] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: an overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [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: 2302.06688
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
Ashkenazi, S., Chakraborty, S., Ma, Z. et al. Linear response of entanglement entropy to \( T\overline{T} \) in massive QFTs. J. High Energ. Phys. 2023, 77 (2023). https://doi.org/10.1007/JHEP04(2023)077
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2023)077