Abstract
We analyse the \( T\overline{T} \) deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve \( T\overline{T} \), \( J\overline{T} \) and \( T\overline{J} \) simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.
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References
J. L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories, Nucl. Phys. B 270 (1986) 186 [INSPIRE].
S. Hellerman, A Universal Inequality for CFT and Quantum Gravity, JHEP 08 (2011) 130 [arXiv:0902.2790] [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].
L. Apolo and W. Song, Strings on warped AdS3 via \( \mathrm{T}\overline{\mathrm{J}} \) deformations, JHEP 10 (2018) 165 [arXiv:1806.10127] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, \( T\overline{J} \) deformed CFT2 and string theory, JHEP 10 (2018) 057 [arXiv:1806.09667] [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, \( T\overline{T} \), \( J\overline{T} \), \( T\overline{J} \) and String Theory, J. Phys. A 52 (2019) 384003 [arXiv:1905.00051] [INSPIRE].
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].
P. Kraus, J. Liu and D. Marolf, Cutoff AdS3 versus the \( T\overline{T} \) deformation, JHEP 07 (2018) 027 [arXiv:1801.02714] [INSPIRE].
P. Caputa, S. Datta, Y. Jiang and P. Kraus, Geometrizing \( T\overline{T} \), JHEP 03 (2021) 140 [arXiv:2011.04664] [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].
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. Dubovsky, V. Gorbenko and G. Hernández-Chifflet, \( T\overline{T} \) partition function from topological gravity, JHEP 09 (2018) 158 [arXiv:1805.07386] [INSPIRE].
J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [arXiv:1801.06895] [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].
R. Conti, S. Negro and R. Tateo, The \( T\overline{T} \) perturbation and its geometric interpretation, JHEP 02 (2019) 085 [arXiv:1809.09593] [INSPIRE].
J. Aguilera-Damia, V. I. Giraldo-Rivera, E. A. Mazenc, I. Salazar Landea and R. M. Soni, A path integral realization of joint \( J\overline{T} \) , \( T\overline{J} \) and \( T\overline{T} \) flows, JHEP 07 (2020) 085 [arXiv:1910.06675] [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].
A. Hashimoto and D. Kutasov, Strings, symmetric products, \( T\overline{T} \) deformations and Hecke operators, Phys. Lett. B 806 (2020) 135479 [arXiv:1909.11118] [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].
S. Hirano and M. Shigemori, Random boundary geometry and gravity dual of \( T\overline{T} \) deformation, JHEP 11 (2020) 108 [arXiv:2003.06300] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, A solvable irrelevant deformation of AdS3/CFT2, JHEP 12 (2017) 155 [arXiv:1707.05800] [INSPIRE].
M. Asrat, A. Giveon, N. Itzhaki and D. Kutasov, Holography Beyond AdS, Nucl. Phys. B 932 (2018) 241 [arXiv:1711.02690] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, \( T\overline{T} \), black holes and negative strings, JHEP 09 (2020) 057 [arXiv:2006.13249] [INSPIRE].
S. Chakraborty, A. Giveon and D. Kutasov, Strings in irrelevant deformations of AdS3/CFT2, JHEP 11 (2020) 057 [arXiv:2009.03929] [INSPIRE].
P. Kraus, R. Monten and R. M. Myers, 3D Gravity in a Box, arXiv:2103.13398 [INSPIRE].
M. Guica and R. Monten, Infinite pseudo-conformal symmetries of classical \( T\overline{T} \), \( J\overline{T} \) and JTa-deformed CFTs, arXiv:2011.05445 [INSPIRE].
M. Guica, Symmetries versus the spectrum of \( J\overline{T} \)-deformed CFTs, SciPost Phys. 10 (2021) 065 [arXiv:2012.15806] [INSPIRE].
H. Ouyang and H. Shu, \( T\overline{T} \) deformation of chiral bosons and Chern-Simons AdS3 gravity, Eur. Phys. J. C 80 (2020) 1155 [arXiv:2006.10514] [INSPIRE].
T. Anous and M. Guica, A general definition of JTa-deformed QFTs, SciPost Phys. 10 (2021) 096 [arXiv:1911.02031] [INSPIRE].
A. A. Bytsenko, L. Vanzo and S. Zerbini, Ray-Singer torsion for a hyperbolic three manifold and asymptotics of Chern-Simons Witten invariant, Nucl. Phys. B 505 (1997) 641 [hep-th/9704035] [INSPIRE].
A. A. Bytsenko, L. Vanzo and S. Zerbini, Quantum correction to the entropy of the (2 + 1)-dimensional black hole, Phys. Rev. D 57 (1998) 4917 [gr-qc/9710106] [INSPIRE].
R. B. Mann and S. N. Solodukhin, Quantum scalar field on three-dimensional (BTZ) black hole instanton: Heat kernel, effective action and thermodynamics, Phys. Rev. D 55 (1997) 3622 [hep-th/9609085] [INSPIRE].
S. Giombi, A. Maloney and X. Yin, One-loop Partition Functions of 3D Gravity, JHEP 08 (2008) 007 [arXiv:0804.1773] [INSPIRE].
J. R. David, M. R. Gaberdiel and R. Gopakumar, The Heat Kernel on AdS3 and its Applications, JHEP 04 (2010) 125 [arXiv:0911.5085] [INSPIRE].
J. Cotler and K. Jensen, A theory of reparameterizations for AdS3 gravity, JHEP 02 (2019) 079 [arXiv:1808.03263] [INSPIRE].
F. Denef, S. A. Hartnoll and S. Sachdev, Black hole determinants and quasinormal modes, Class. Quant. Grav. 27 (2010) 125001 [arXiv:0908.2657] [INSPIRE].
S. Datta and J. R. David, Higher Spin Quasinormal Modes and One-Loop Determinants in the BTZ black Hole, JHEP 03 (2012) 079 [arXiv:1112.4619] [INSPIRE].
A. Castro, C. Keeler and P. Szepietowski, Tweaking one-loop determinants in AdS3, JHEP 10 (2017) 070 [arXiv:1707.06245] [INSPIRE].
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Datta, S., Jiang, Y. Characters of irrelevant deformations. J. High Energ. Phys. 2021, 162 (2021). https://doi.org/10.1007/JHEP07(2021)162
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DOI: https://doi.org/10.1007/JHEP07(2021)162