Abstract
A solvable irrelevant deformation of AdS3/CFT2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable \( T\overline{T} \) deformations of two-dimensional CFTs. Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 in the IR and a linear dilaton vacuum of little string theory in the UV. The insertion of the operator that realizes the deformation in the correlation functions produces a logarithmic divergence, leading to the renormalization of the primary operators, which thus acquire an anomalous dimension. We compute this anomalous dimension explicitly, and this provides us with a direct way of determining the spectrum of the theory. We discuss this and other features of the correlation functions in presence of the deformation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Giveon, N. Itzhaki and D. Kutasov, \( T\overline{T} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [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].
O. Aharony, M. Berkooz, D. Kutasov and N. Seiberg, Linear dilatons, NS five-branes and holography, JHEP 10 (1998) 004 [hep-th/9808149] [INSPIRE].
A. Giveon, D. Kutasov and O. Pelc, Holography for noncritical superstrings, JHEP 10 (1999) 035 [hep-th/9907178] [INSPIRE].
A. Giveon and D. Kutasov, Little string theory in a double scaling limit, JHEP 10 (1999) 034 [hep-th/9909110] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS 2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, A solvable irrelevant deformation of AdS 3 /CFT 2, JHEP 12 (2017) 155 [arXiv:1707.05800] [INSPIRE].
A. Giveon, D. Kutasov and N. Seiberg, Comments on string theory on AdS 3, Adv. Theor. Math. Phys. 2 (1998) 733 [hep-th/9806194] [INSPIRE].
D. Kutasov and N. Seiberg, More comments on string theory on AdS 3, JHEP 04 (1999) 008 [hep-th/9903219] [INSPIRE].
A. Giveon and D. Kutasov, Notes on AdS 3, Nucl. Phys. B 621 (2002) 303 [hep-th/0106004] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS 3 and SL(2, ℝ) WZW model 1.: The spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [INSPIRE].
G. Giribet and C.A. Núñez, Correlators in AdS 3 string theory, JHEP 06 (2001) 010 [hep-th/0105200] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS 3 and the SL(2, ℝ) WZW model. Part 3. Correlation functions, Phys. Rev. D 65 (2002) 106006 [hep-th/0111180] [INSPIRE].
M.R. Gaberdiel and I. Kirsch, Worldsheet correlators in AdS 3 /CF T 2, JHEP 04 (2007) 050 [hep-th/0703001] [INSPIRE].
A. Dabholkar and A. Pakman, Exact chiral ring of AdS 3 /CF T 2, Adv. Theor. Math. Phys. 13 (2009) 409 [hep-th/0703022] [INSPIRE].
G. Giribet, A. Pakman and L. Rastelli, Spectral Flow in AdS 3 /CF T 2, JHEP 06 (2008) 013 [arXiv:0712.3046] [INSPIRE].
C.A. Cardona and C.A. Núñez, Three-point functions in superstring theory on AdS 3 × S 3 × T 4, JHEP 06 (2009) 009 [arXiv:0903.2001] [INSPIRE].
D. Israel, C. Kounnas and M.P. Petropoulos, Superstrings on NS5 backgrounds, deformed AdS 3 and holography, JHEP 10 (2003) 028 [hep-th/0306053] [INSPIRE].
M. Wakimoto, Fock representations of the affine lie algebra A1(1), Commun. Math. Phys. 104 (1986) 605 [INSPIRE].
N. Ishibashi, K. Okuyama and Y. Satoh, Path integral approach to string theory on AdS 3, Nucl. Phys. B 588 (2000) 149 [hep-th/0005152] [INSPIRE].
S. Ribault and J. Teschner, H+(3)-WZNW correlators from Liouville theory, JHEP 06 (2005) 014 [hep-th/0502048] [INSPIRE].
Y. Hikida and V. Schomerus, H+(3) WZNW model from Liouville field theory, JHEP 10 (2007) 064 [arXiv:0706.1030] [INSPIRE].
J. Parsons and S.F. Ross, Strings in extremal BTZ black holes, JHEP 04 (2009) 134 [arXiv:0901.3044] [INSPIRE].
M. Asrat, A. Giveon, N. Itzhaki and D. Kutasov, Holography Beyond AdS, arXiv:1711.02690 [INSPIRE].
K. Becker and M. Becker, Interactions in the SL(2,IR)/U(1) black hole background, Nucl. Phys. B 418 (1994) 206 [hep-th/9310046] [INSPIRE].
V.S. Dotsenko and V.A. Fateev, Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c ¡ 1, Nucl. Phys. B 251 (1985) 691 [INSPIRE].
P. Di Francesco and D. Kutasov, World sheet and space-time physics in two-dimensional (Super)string theory, Nucl. Phys. B 375 (1992) 119 [hep-th/9109005] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, Stringy Horizons, JHEP 06 (2015) 064 [arXiv:1502.03633] [INSPIRE].
S. Ribault, A family of solvable non-rational conformal field theories, JHEP 05 (2008) 073 [arXiv:0803.2099] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, Stringy Horizons II, JHEP 10 (2016) 157 [arXiv:1603.05822] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), 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].
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: 1711.02716
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Giribet, G. \( T\overline{T} \)-deformations, AdS/CFT and correlation functions. J. High Energ. Phys. 2018, 114 (2018). https://doi.org/10.1007/JHEP02(2018)114
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)114