Cutoff AdS3 versus TT¯ CFT2 in the large central charge sector: correlators of energy-momentum tensor

Yi Li; Yang Zhou

doi:10.1007/JHEP12(2020)168

. 2020 Dec 28;2020(12):168. doi: 10.1007/JHEP12(2020)168

Cutoff AdS₃ versus $T \bar{T}$ CFT₂ in the large central charge sector: correlators of energy-momentum tensor

Yi Li ^1,^✉, Yang Zhou ¹

PMCID: PMC7769565 PMID: 33390725

Abstract

In this article we probe the proposed holographic duality between $T \bar{T}$ deformed two dimensional conformal field theory and the gravity theory of AdS₃ with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $T \bar{T}$ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS₃ with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $T \bar{T}$ CFT parameters.

Keywords: AdS-CFT Correspondence, Conformal Field Theory

Footnotes

ArXiv ePrint: 2005.01693

Publisher’s Note

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Contributor Information

Yi Li, Email: liyi@fudan.edu.cn.

Yang Zhou, Email: yang_zhou@fudan.edu.cn.

References

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[32].L.V. Iliesiu, J. Kruthoff, G.J. Turiaci and H. Verlinde, JT gravity at finite cutoff, arXiv:2004.07242 [INSPIRE].
[33].G. Jafari, A. Naseh and H. Zolfi, Path Integral Optimization for $T \bar{T}$ Deformation, Phys. Rev. D101 (2020) 026007 [arXiv:1909.02357] [INSPIRE].
[34].Kraus P, Liu J, Marolf D. Cutoff AdS3versus the $T \bar{T}$ deformation. JHEP. 2018;07:027. doi: 10.1007/JHEP07(2018)027. [DOI] [Google Scholar]
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[37].M. Guica and R. Monten, $T \bar{T}$ and the mirage of a bulk cutoff, arXiv:1906.11251 [INSPIRE].
[38].Aharony O, Vaknin T. The TT*deformation at large central charge. JHEP. 2018;05:166. [Google Scholar]
[39].Y. Jiang, Lectures on solvable irrelevant deformations of 2d quantum field theory, arXiv:1904.13376 [INSPIRE].
[40].B. Allen and T. Jacobson, Vector Two Point Functions in Maximally Symmetric Spaces, Commun. Math. Phys.103 (1986) 669 [INSPIRE].
[41].Osborn H, Shore GM. Correlation functions of the energy momentum tensor on spaces of constant curvature. Nucl. Phys. B. 2000;571:287. doi: 10.1016/S0550-3213(99)00775-0. [DOI] [Google Scholar]
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[CR1] [1].Smirnov FA, Zamolodchikov AB. On space of integrable quantum field theories. Nucl. Phys. B. 2017;915:363. doi: 10.1016/j.nuclphysb.2016.12.014. [DOI] [Google Scholar]

[CR2] [2].Conti R, Iannella L, Negro S, Tateo R. Generalised Born-Infeld models, Lax operators and the $T \bar{T}$ perturbation. JHEP. 2018;11:007. doi: 10.1007/JHEP11(2018)007. [DOI] [Google Scholar]

[CR3] [3].A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, $T \bar{T}$ -deformed 2D Quantum Field Theories, JHEP10 (2016) 112 [arXiv:1608.05534] [INSPIRE].

[CR4] [4].Dubovsky S, Gorbenko V, Mirbabayi M. Asymptotic fragility, near AdS2holography and $T \bar{T}$ . JHEP. 2017;09:136. doi: 10.1007/JHEP09(2017)136. [DOI] [Google Scholar]

[CR5] [5].A.B. Zamolodchikov, Expectation value of composite field $T \bar{T}$ in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].

[CR6] [6].S. Datta and Y. Jiang, $T \bar{T}$ deformed partition functions, JHEP08 (2018) 106 [arXiv:1806.07426] [INSPIRE].

[CR7] [7].Aharony O, Datta S, Giveon A, Jiang Y, Kutasov D. Modular invariance and uniqueness of $T \bar{T}$ deformed CFT. JHEP. 2019;01:086. doi: 10.1007/JHEP01(2019)086. [DOI] [Google Scholar]

[CR8] [8].Cardy J. The $T \bar{T}$ deformation of quantum field theory as random geometry. JHEP. 2018;10:186. doi: 10.1007/JHEP10(2018)186. [DOI] [Google Scholar]

[CR9] [9].S. Dubovsky, V. Gorbenko and G. Hernández-Chifflet, $T \bar{T}$ partition function from topological gravity, JHEP09 (2018) 158 [arXiv:1805.07386] [INSPIRE].

[CR10] [10].J. Cardy, $T \bar{T}$ deformation of correlation functions, JHEP12 (2019) 160 [arXiv:1907.03394] [INSPIRE].

[CR11] [11].He S, Shu H. Correlation functions, entanglement and chaos in the $T \bar{T} / J \bar{T}$ –deformed CFTs. JHEP. 2020;02:088. doi: 10.1007/JHEP02(2020)088. [DOI] [Google Scholar]

[CR12] [12].S. He and Y. Sun, Correlation functions of CFTs on a torus with a $T \bar{T}$ deformation, Phys. Rev. D102 (2020) 026023 [arXiv:2004.07486] [INSPIRE].

[CR13] [13].Jiang Y. Expectation value of $T \bar{T}$ operator in curved spacetimes. JHEP. 2020;02:094. doi: 10.1007/JHEP02(2020)094. [DOI] [Google Scholar]

[CR14] [14].T.D. Brennan, C. Ferko, E. Martinec and S. Sethi, Defining the $T \bar{T}$ Deformation on AdS₂, arXiv:2005.00431 [INSPIRE].

[CR15] [15].A.J. Tolley, $T \bar{T}$ deformations, massive gravity and non-critical strings, JHEP06 (2020) 050 [arXiv:1911.06142] [INSPIRE].

[CR16] [16].E.A. Mazenc, V. Shyam and R.M. Soni, A $T \bar{T}$ Deformation for Curved Spacetimes from 3d Gravity, arXiv:1912.09179 [INSPIRE].

[CR17] [17].McGough L, Mezei M, Verlinde H. Moving the CFT into the bulk with $T \bar{T}$ . JHEP. 2018;04:010. doi: 10.1007/JHEP04(2018)010. [DOI] [Google Scholar]

[CR18] [18].Donnelly W, Shyam V. Entanglement entropy and $T \bar{T}$ deformation. Phys. Rev. Lett. 2018;121:131602. doi: 10.1103/PhysRevLett.121.131602. [DOI] [PubMed] [Google Scholar]

[CR19] [19].B. Chen, L. Chen and P.-X. Hao, Entanglement entropy in $T \bar{T}$ -deformed CFT, Phys. Rev. D98 (2018) 086025 [arXiv:1807.08293] [INSPIRE].

[CR20] [20].Banerjee A, Bhattacharyya A, Chakraborty S. Entanglement Entropy for $T \bar{T}$ deformed CFT in general dimensions. Nucl. Phys. B. 2019;948:114775. doi: 10.1016/j.nuclphysb.2019.114775. [DOI] [Google Scholar]

[CR21] [21].Jeong H-S, Kim K-Y, Nishida M. Entanglement and Rényi entropy of multiple intervals in $T \bar{T}$ -deformed CFT and holography. Phys. Rev. D. 2019;100:106015. doi: 10.1103/PhysRevD.100.106015. [DOI] [Google Scholar]

[CR22] [22].Grieninger S. Entanglement entropy and $T \bar{T}$ deformations beyond antipodal points from holography. JHEP. 2019;11:171. doi: 10.1007/JHEP11(2019)171. [DOI] [Google Scholar]

[CR23] [23].A. Lewkowycz, J. Liu, E. Silverstein and G. Torroba, $T \bar{T}$ and EE, with implications for (A)dS subregion encodings, JHEP04 (2020) 152 [arXiv:1909.13808] [INSPIRE].

[CR24] [24].Geng H. Some Information Theoretic Aspects of De-Sitter Holography. JHEP. 2020;02:005. doi: 10.1007/JHEP02(2020)005. [DOI] [Google Scholar]

[CR25] [25].Donnelly W, LePage E, Li Y-Y, Pereira A, Shyam V. Quantum corrections to finite radius holography and holographic entanglement entropy. JHEP. 2020;05:006. doi: 10.1007/JHEP05(2020)006. [DOI] [Google Scholar]

[CR26] [26].G. Bonelli, N. Doroud and M. Zhu, $T \bar{T}$ -deformations in closed form, JHEP06 (2018) 149 [arXiv:1804.10967] [INSPIRE].

[CR27] [27].M. Taylor, TT deformations in general dimensions, arXiv:1805.10287 [INSPIRE].

[CR28] [28].Hartman T, Kruthoff J, Shaghoulian E, Tajdini A. Holography at finite cutoff with a T2deformation. JHEP. 2019;03:004. doi: 10.1007/JHEP03(2019)004. [DOI] [Google Scholar]

[CR29] [29].Caputa P, Datta S, Shyam V. Sphere partition functions & cut-off AdS. JHEP. 2019;05:112. doi: 10.1007/JHEP05(2019)112. [DOI] [Google Scholar]

[CR30] [30].D.J. Gross, J. Kruthoff, A. Rolph and E. Shaghoulian, $T \bar{T}$ in AdS₂and Quantum Mechanics, Phys. Rev. D101 (2020) 026011 [arXiv:1907.04873] [INSPIRE].

[CR31] [31].D.J. Gross, J. Kruthoff, A. Rolph and E. Shaghoulian, Hamiltonian deformations in quantum mechanics, $T \bar{T}$ , and the SYK model, Phys. Rev. D102 (2020) 046019 [arXiv:1912.06132] [INSPIRE].

[CR32] [32].L.V. Iliesiu, J. Kruthoff, G.J. Turiaci and H. Verlinde, JT gravity at finite cutoff, arXiv:2004.07242 [INSPIRE].

[CR33] [33].G. Jafari, A. Naseh and H. Zolfi, Path Integral Optimization for $T \bar{T}$ Deformation, Phys. Rev. D101 (2020) 026007 [arXiv:1909.02357] [INSPIRE].

[CR34] [34].Kraus P, Liu J, Marolf D. Cutoff AdS3versus the $T \bar{T}$ deformation. JHEP. 2018;07:027. doi: 10.1007/JHEP07(2018)027. [DOI] [Google Scholar]

[CR35] [35].Heemskerk I, Polchinski J. Holographic and Wilsonian Renormalization Groups. JHEP. 2011;06:031. doi: 10.1007/JHEP06(2011)031. [DOI] [Google Scholar]

[CR36] [36].Faulkner T, Liu H, Rangamani M. Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm. JHEP. 2011;08:051. [Google Scholar]

[CR37] [37].M. Guica and R. Monten, $T \bar{T}$ and the mirage of a bulk cutoff, arXiv:1906.11251 [INSPIRE].

[CR38] [38].Aharony O, Vaknin T. The TT*deformation at large central charge. JHEP. 2018;05:166. [Google Scholar]

[CR39] [39].Y. Jiang, Lectures on solvable irrelevant deformations of 2d quantum field theory, arXiv:1904.13376 [INSPIRE].

[CR40] [40].B. Allen and T. Jacobson, Vector Two Point Functions in Maximally Symmetric Spaces, Commun. Math. Phys.103 (1986) 669 [INSPIRE].

[CR41] [41].Osborn H, Shore GM. Correlation functions of the energy momentum tensor on spaces of constant curvature. Nucl. Phys. B. 2000;571:287. doi: 10.1016/S0550-3213(99)00775-0. [DOI] [Google Scholar]

[CR42] [42].Skenderis K, Solodukhin SN. Quantum effective action from the AdS/CFT correspondence. Phys. Lett. B. 2000;472:316. doi: 10.1016/S0370-2693(99)01467-7. [DOI] [Google Scholar]

[CR43] [43].Henningson M, Skenderis K. The Holographic Weyl anomaly. JHEP. 1998;07:023. doi: 10.1088/1126-6708/1998/07/023. [DOI] [Google Scholar]

[CR44] [44].de Haro S, Solodukhin SN, Skenderis K. Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence. Commun. Math. Phys. 2001;217:595. doi: 10.1007/s002200100381. [DOI] [Google Scholar]

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Cutoff AdS₃ versus $T \bar{T}$ CFT₂ in the large central charge sector: correlators of energy-momentum tensor

Yi Li

Yang Zhou

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Cutoff AdS3 versus TT¯ CFT2 in the large central charge sector: correlators of energy-momentum tensor

Yi Li

Yang Zhou

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Cutoff AdS₃ versus $T \bar{T}$ CFT₂ in the large central charge sector: correlators of energy-momentum tensor