Abstract
In this paper we prove the equivalence among (i) the weakly coupled worldsheet string theory described by the coset sigma model \( \frac{\mathrm{SL}{\left(2,\mathrm{\mathbb{R}}\right)}_k\times \mathrm{U}(1)}{\mathrm{U}(1)} \) × S3 × T4 with SL(2, ℝ) WZW level k ≥ 2, (ii) the full near horizon theory of the NS5 branes with k NS5 branes wrapping T4 × S1, p » 1 F1 strings wrapping S1 and n units of momentum along the S1 and (iii) the single trace \( T\overline{T} \) deformation of string theory in AdS3 × S3 × T4. As a check we compute the spectrum (continuous) of the spacetime theory by performing BRST quantization of the coset description of the worldsheet theory and show that it matches exactly with the one derived in the case of single trace \( T\overline{T} \) deformed string theory in AdS3. Secondly, we compute the two-point correlation function of local operators of the spacetime theory using the worldsheet coset approach and reproduce the same two-point function from the supergravity approach.
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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].
A. Giveon, N. Itzhaki and D. Kutasov, \( \mathrm{T}\overline{\mathrm{T}} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [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].
G. Giribet, \( T\overline{T} \)-deformations, AdS/CFT and correlation functions, JHEP 02 (2018) 114 [arXiv:1711.02716] [INSPIRE].
S. Chakraborty, A. Giveon, N. Itzhaki and D. Kutasov, Entanglement beyond AdS, Nucl. Phys. B 935 (2018) 290 [arXiv:1805.06286] [INSPIRE].
S. Chakraborty, Wilson loop in a \( T\overline{T} \) like deformed CFT2, Nucl. Phys. B 938 (2019) 605 [arXiv:1809.01915] [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, A. Giveon and D. Kutasov, \( T\overline{T} \), black holes and negative strings, JHEP 09 (2020) 057 [arXiv:2006.13249] [INSPIRE].
S. Chakraborty, G. Katoch and S.R. Roy, Holographic Complexity of LST and Single Trace \( T\overline{T} \), arXiv:2012.11644 [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, \( J\overline{T} \) deformed CFT2 and string theory, JHEP 10 (2018) 057 [arXiv:1806.09667] [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].
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].
S. Chakraborty, A. Giveon and D. Kutasov, Strings in irrelevant deformations of AdS3/CFT2, JHEP 11 (2020) 057 [arXiv:2009.03929] [INSPIRE].
S. Chakraborty and A. Hashimoto, Entanglement entropy for \( \mathrm{T}\overline{\mathrm{T}},\mathrm{J}\overline{\mathrm{T}},\mathrm{T}\overline{\mathrm{J}} \) deformed holographic CFT, JHEP 02 (2021) 096 [arXiv:2010.15759] [INSPIRE].
S. Carlip, Conformal field theory, (2 + 1)-dimensional gravity, and the BTZ black hole, Class. Quant. Grav. 22 (2005) R85 [gr-qc/0503022] [INSPIRE].
R. Dijkgraaf, H.L. Verlinde and E.P. Verlinde, String propagation in a black hole geometry, Nucl. Phys. B 371 (1992) 269 [INSPIRE].
A. Giveon, E. Rabinovici and A. Sever, Beyond the singularity of the 2 − D charged black hole, JHEP 07 (2003) 055 [hep-th/0305140] [INSPIRE].
A. Giveon, D. Kutasov, E. Rabinovici and A. Sever, Phases of quantum gravity in AdS3 and linear dilaton backgrounds, Nucl. Phys. B 719 (2005) 3 [hep-th/0503121] [INSPIRE].
A. Giveon and D. Kutasov, Fundamental strings and black holes, JHEP 01 (2007) 071 [hep-th/0611062] [INSPIRE].
A. Giveon, Comments on \( T\overline{T} \), \( J\overline{T} \) and String Theory, arXiv:1903.06883 [INSPIRE].
M. Baggio and A. Sfondrini, Strings on NS-NS Backgrounds as Integrable Deformations, Phys. Rev. D 98 (2018) 021902 [arXiv:1804.01998] [INSPIRE].
A. Dei and A. Sfondrini, Integrable spin chain for stringy Wess-Zumino-Witten models, JHEP 07 (2018) 109 [arXiv:1806.00422] [INSPIRE].
A. Giveon, D. Kutasov and N. Seiberg, Comments on string theory on AdS3, Adv. Theor. Math. Phys. 2 (1998) 733 [hep-th/9806194] [INSPIRE].
D. Kutasov and N. Seiberg, More comments on string theory on AdS3, JHEP 04 (1999) 008 [hep-th/9903219] [INSPIRE].
A. Giveon and D. Kutasov, Notes on AdS3, Nucl. Phys. B 621 (2002) 303 [hep-th/0106004] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and SL(2, ℝ) WZW model. Part 1: The Spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [INSPIRE].
J.M. Maldacena, H. Ooguri and J. Son, Strings in AdS3 and the SL(2, ℝ) WZW model. Part 2. Euclidean black hole, J. Math. Phys. 42 (2001) 2961 [hep-th/0005183] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and the SL(2, ℝ) WZW model. Part 3. Correlation functions, Phys. Rev. D 65 (2002) 106006 [hep-th/0111180] [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
S. Förste, A Truly marginal deformation of SL(2, R) in a null direction, Phys. Lett. B 338 (1994) 36 [hep-th/9407198] [INSPIRE].
D. Israel, C. Kounnas and M.P. Petropoulos, Superstrings on NS5 backgrounds, deformed AdS3 and holography, JHEP 10 (2003) 028 [hep-th/0306053] [INSPIRE].
M. Goykhman and A. Parnachev, Stringy holography at finite density, Nucl. Phys. B 874 (2013) 115 [arXiv:1304.4496] [INSPIRE].
D. Karabali and H.J. Schnitzer, BRST Quantization of the Gauged WZW Action and Coset Conformal Field Theories, Nucl. Phys. B 329 (1990) 649 [INSPIRE].
A.A. Tseytlin, Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories, Nucl. Phys. B 411 (1994) 509 [hep-th/9302083] [INSPIRE].
F. Bastianelli, BRST symmetry from a change of variables and the gauged WZNW models, Nucl. Phys. B 361 (1991) 555 [INSPIRE].
S. Elitzur, A. Giveon, D. Kutasov and E. Rabinovici, From big bang to big crunch and beyond, JHEP 06 (2002) 017 [hep-th/0204189] [INSPIRE].
J. Parsons and S.F. Ross, Strings in extremal BTZ black holes, JHEP 04 (2009) 134 [arXiv:0901.3044] [INSPIRE].
R. Argurio, A. Giveon and A. Shomer, Superstrings on AdS3 and symmetric products, JHEP 12 (2000) 003 [hep-th/0009242] [INSPIRE].
A. Sfondrini and S.J. van Tongeren, \( T\overline{T} \) deformations as TsT transformations, Phys. Rev. D 101 (2020) 066022 [arXiv:1908.09299] [INSPIRE].
S. Chakraborty and A. Hashimoto, Thermodynamics of \( \mathrm{T}\overline{\mathrm{T}},\mathrm{J}\overline{\mathrm{T}},\mathrm{T}\overline{\mathrm{J}} \) deformed conformal field theories, JHEP 07 (2020) 188 [arXiv:2006.10271] [INSPIRE].
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Chakraborty, S. \( \frac{\mathrm{SL}\left(2,\mathrm{\mathbb{R}}\right)\times \mathrm{U}(1)}{\mathrm{U}(1)} \) CFT, NS5+F1 system and single trace \( T\overline{T} \). J. High Energ. Phys. 2021, 113 (2021). https://doi.org/10.1007/JHEP03(2021)113
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DOI: https://doi.org/10.1007/JHEP03(2021)113