TsT, $$ \mathrm{T}\overline{\mathrm{T}} $$ and black strings

Abstract

We study the relationship between TsT transformations, marginal deformations of string theory on AdS 3 backgrounds, and irrelevant deformations of 2d CFTs. We show that TsT transformations of NS-NS backgrounds correspond to instantaneous deformations of the worldsheet action by the antisymmetric product of two Noether currents, holographically mirroring the definition of the TT , JT , TJ, and JJ deformations of 2d CFTs. Applying a TsT transformation to string theory on BTZ ×S 3 × M 4 we obtain a general class of rotating black string solutions, including the Horne-Horowitz and the Giveon-Itzhaki-Kutasov ones as special cases, which we show are holographically dual to thermal states in single-trace TT-deformed CFTs. We also find a smooth solution interpolating between global AdS 3 in the IR and a linear dilaton background in the UV that is interpreted as the NS-NS ground state in the dual TT-deformed CFT. This background suggests the existence of an upper bound on the deformation parameter above which the solution becomes complex. We find that the worldsheet spectrum, the thermodynamics of the black strings (in particular their Bekenstein-Hawking entropy), and the critical value of the deformation parameter match the corresponding quantities obtained from single-trace TT deformations.

Correlation functions of CFTs on a torus with a TT¯ deformation

“…Besides TT deformation, other deformations in this set including the so-called JT deformation also receive much attention from both field theory and holographic points of view [12][13][14][15][16][17][18][19][20]. In addition, the TT deformation can also be understood from some other perspectives and generalizations [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

Thermodynamics of $$ \mathrm{T}\overline{\mathrm{T}} $$, $$ \mathrm{J}\overline{\mathrm{T}} $$, $$ \mathrm{T}\overline{\mathrm{J}} $$ deformed conformal field theories

“…Since the area of this torus was directly proportional to the area of the horizon, the thermodynamic relations turned out to be insensitive to the twist. One exception to this pattern of behavior can be found in the T-s-T interpretation of the pure TT deformation discussed in [22]. Upon closer look, one sees that the T-s-T transformation discussed in section 3.2 of [22] involves twisting a torus that involves both spatial and temporal directions.…”

“…One exception to this pattern of behavior can be found in the T-s-T interpretation of the pure TT deformation discussed in [22]. Upon closer look, one sees that the T-s-T transformation discussed in section 3.2 of [22] involves twisting a torus that involves both spatial and temporal directions. (Strictly speaking, the authors of [22] twisted and T-dualized along a light like direction, but this can be viewed as a space-like T-duality and a time-like twist that is infinitely boosted.)…”

“…The thermodynamics of this system can then be read off from the property of the horizon and the analysis of the conical singularity of the Euclidean solution. The intermediate steps of this analysis is somewhat cumbersome, but we will be brief here as the analysis is standard and it was essentially carried out in [12,22]. The essential step is to solve for r 0 from (2.50) of [21] T (r 0 ) = 1 2πr 0 cosh α cosh γ cosh σ…”

Analytic integrability for holographic duals with $$ J\overline{T} $$ deformations

“…Our recent understanding on gauge/string correspondence has revealed a remarkable duality between string sigma models on warped AdS 3 × S 3 [1][2][3][4] and solvable irrelevant deformations [5][6][7][8][9][10][11][12][13][14] in 2D CFTs [15][16][17][18][19][20]. The stringy side of the duality is obtained via marginal deformations of the AdS 3 × S 3 world-sheet theory by suitable choice of vertex operators 1 those are observables with scaling dimension (1,2) in the boundary CFT 2 [20], where x(= ϕ + t) andx(= ϕ − t) are respectively the left and right moving coordinates associated with the dual CFT.…”