Abstract
We calculate quantum corrections to holographic entanglement entropy in the proposed duality between \( T\overline{T} \)-deformed holographic 2D CFTs and gravity in AdS3 with a finite cutoff. We first establish the dictionary between the two theories by mapping the flow equation of the deformed CFT to the bulk Wheeler-DeWitt equation. The latter reduces to an ordinary differential equation for the sphere partition function, which we solve to find the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere. The entanglement entropy in the inverse central charge expansion yields the expectation value of the bulk length operator plus the entropy of length fluctuations, in accordance with the Ryu-Takayanagi formula and its generalization due to Faulkner, Lewkowycz, and Maldacena. Special attention is paid to the conformal mode problem and its resolution by a choice of contour for the gravitational path integral.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
V. Shyam, Background independent holographic dual to \( T\overline{T} \)deformed CFT with large central charge in 2 dimensions, JHEP 10 (2017) 108 [arXiv:1707.08118] [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].
J. Cardy, The \( T\overline{T} \)deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [arXiv:1801.06895] [INSPIRE].
S. Dubovsky, V. Gorbenko and G. Hernández-Chifflet, \( T\overline{T} \)partition function from topological gravity, JHEP 09 (2018) 158 [arXiv:1805.07386] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS2 holography and \( T\overline{T} \) , JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
S. Datta and Y. Jiang, \( T\overline{T} \)deformed partition functions, JHEP 08 (2018) 106 [arXiv:1806.07426] [INSPIRE].
O. Aharony, S. Datta, A. Giveon, Y. Jiang and D. Kutasov, Modular invariance and uniqueness of \( T\overline{T} \)deformed CFT, JHEP 01 (2019) 086 [arXiv:1808.02492] [INSPIRE].
P. Kraus, J. Liu and D. Marolf, Cutoff AdS3 versus the \( T\overline{T} \)deformation, JHEP 07 (2018) 027 [arXiv:1801.02714] [INSPIRE].
M. Taylor, TT deformations in general dimensions, arXiv:1805.10287 [INSPIRE].
T. Hartman, J. Kruthoff, E. Shaghoulian and A. Tajdini, Holography at finite cutoff with a T2 deformation, JHEP 03 (2019) 004 [arXiv:1807.11401] [INSPIRE].
V. Shyam, Finite Cutoff AdS5 Holography and the Generalized Gradient Flow, JHEP 12 (2018) 086 [arXiv:1808.07760] [INSPIRE].
P. Caputa, S. Datta and V. Shyam, Sphere partition functions & cut-off AdS, JHEP 05 (2019) 112 [arXiv:1902.10893] [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].
C. Murdia, Y. Nomura, P. Rath and N. Salzetta, Comments on holographic entanglement entropy in TT deformed conformal field theories, Phys. Rev. D 100 (2019) 026011 [arXiv:1904.04408] [INSPIRE].
W. Donnelly and V. Shyam, Entanglement entropy and \( T\overline{T} \)deformation, Phys. Rev. Lett. 121 (2018) 131602 [arXiv:1806.07444] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
X. Dong, The Gravity Dual of Renyi Entropy, Nature Commun. 7 (2016) 12472 [arXiv:1601.06788] [INSPIRE].
A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \)in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
Y. Jiang, Expectation value of \( \mathrm{T}\overline{\mathrm{T}} \)operator in curved spacetimes, JHEP 02 (2020) 094 [arXiv:1903.07561] [INSPIRE].
V. Moncrief, Reduction of the Einstein equations in (2 + 1)-dimensions to a Hamiltonian system over Teichmüller space, J. Math. Phys. 30 (1989) 2907 [INSPIRE].
Y. Fujiwara and J. Soda, Teichmüller Motion of (2 + 1)-dimensional Gravity With the Cosmological Constant, Prog. Theor. Phys. 83 (1990) 733 [INSPIRE].
P. Caputa and S. Hirano, Airy Function and 4d Quantum Gravity, JHEP 06 (2018) 106 [arXiv:1804.00942] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
Z. Komargodski, The \( T\overline{T} \)deformation, Second Simons Bootstrap Collaboration School, Caltech (2018) [http://bootstrapcollaboration.com/bootstrap2018/school/].
J. Cardy, \( T\overline{T} \)deformation of correlation functions, JHEP 12 (2019) 160 [arXiv:1907.03394] [INSPIRE].
F.W.J. Olver et al. eds., NIST Digital Library of Mathematical Functions, Release 1.0.18 of 2018-03-27 [http://dlmf.nist.gov/].
V. Gorbenko, E. Silverstein and G. Torroba, dS/dS and \( T\overline{T} \), JHEP 03 (2019) 085 [arXiv:1811.07965] [INSPIRE].
J.J. Halliwell and J.B. Hartle, Integration Contours for the No Boundary Wave Function of the Universe, Phys. Rev. D 41 (1990) 1815 [INSPIRE].
A. Dasgupta and R. Loll, A Proper time cure for the conformal sickness in quantum gravity, Nucl. Phys. B 606 (2001) 357 [hep-th/0103186] [INSPIRE].
P.O. Mazur and E. Mottola, The Gravitational Measure, Solution of the Conformal Factor Problem and Stability of the Ground State of Quantum Gravity, Nucl. Phys. B 341 (1990) 187 [INSPIRE].
G.W. Gibbons, S.W. Hawking and M.J. Perry, Path Integrals and the Indefiniteness of the Gravitational Action, Nucl. Phys. B 138 (1978) 141 [INSPIRE].
T. Bautista, A. Dabholkar and H. Erbin, Quantum Gravity from Timelike Liouville theory, JHEP 10 (2019) 284 [arXiv:1905.12689] [INSPIRE].
I. Aniceto and R. Schiappa, Nonperturbative Ambiguities and the Reality of Resurgent Transseries, Commun. Math. Phys. 335 (2015) 183 [arXiv:1308.1115] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
X. Wen, S. Matsuura and S. Ryu, Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories, Phys. Rev. B 93 (2016) 245140 [arXiv:1603.08534] [INSPIRE].
J.R. Fliss et al., Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory, JHEP 09 (2017) 056 [arXiv:1705.09611] [INSPIRE].
G. Wong, A note on entanglement edge modes in Chern Simons theory, JHEP 08 (2018) 020 [arXiv:1706.04666] [INSPIRE].
E. Witten, (2 + 1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
W. Donnelly and L. Freidel, Local subsystems in gauge theory and gravity, JHEP 09 (2016) 102 [arXiv:1601.04744] [INSPIRE].
L. McGough and H. Verlinde, Bekenstein-Hawking Entropy as Topological Entanglement Entropy, JHEP 11 (2013) 208 [arXiv:1308.2342] [INSPIRE].
M. Geiller, Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity, Nucl. Phys. B 924 (2017) 312 [arXiv:1703.04748] [INSPIRE].
W. Wieland, Fock representation of gravitational boundary modes and the discreteness of the area spectrum, Annales Henri Poincaŕe 18 (2017) 3695 [arXiv:1706.00479] [INSPIRE].
D. Harlow, The Ryu-Takayanagi Formula from Quantum Error Correction, Commun. Math. Phys. 354 (2017) 865 [arXiv:1607.03901] [INSPIRE].
J. Lin, Ryu-Takayanagi Area as an Entanglement Edge Term, arXiv:1704.07763 [INSPIRE].
X. Dong, D. Harlow and D. Marolf, Flat entanglement spectra in fixed-area states of quantum gravity, JHEP 10 (2019) 240 [arXiv:1811.05382] [INSPIRE].
C. Akers and P. Rath, Holographic Renyi Entropy from Quantum Error Correction, JHEP 05 (2019) 052 [arXiv:1811.05171] [INSPIRE].
L. Freidel, Reconstructing AdS/CFT, arXiv:0804.0632 [INSPIRE].
E.A. Mazenc, V. Shyam and R.M. Soni, A \( T\overline{T} \)Deformation for Curved Spacetimes from 3d Gravity, arXiv:1912.09179 [INSPIRE].
S. Grieninger, Entanglement entropy and \( T\overline{T} \)deformations beyond antipodal points from holography, JHEP 11 (2019) 171 [arXiv:1908.10372] [INSPIRE].
E. Witten, A Note On Boundary Conditions In Euclidean Gravity, arXiv:1805.11559 [INSPIRE].
L.V. Iliesiu, S.S. Pufu, H. Verlinde and Y. Wang, An exact quantization of Jackiw-Teitelboim gravity, JHEP 11 (2019) 091 [arXiv:1905.02726] [INSPIRE].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1909.11402
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Donnelly, W., LePage, E., Li, YY. et al. Quantum corrections to finite radius holography and holographic entanglement entropy. J. High Energ. Phys. 2020, 6 (2020). https://doi.org/10.1007/JHEP05(2020)006
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2020)006