TsT, $T\bar{T}$ and black strings

TL;DR

The paper develops a precise holographic dictionary between TsT transformations of NS-NS AdS$_3$ backgrounds and irrelevant, single-trace deformations of 2d CFTs, notably $T\bar{T}$ and $J\bar{T}/T\bar{J}$. It shows TsT acts as an instantaneous worldsheet deformation by the antisymmetric product of two Noether currents and derives the corresponding string spectrum, including its spectral flow structure, which reproduces the single-trace TTbar and TTbar-like deformations. Applying TsT to BTZ$\times S^3\times M^4$ yields rotating black strings whose spectrum and thermodynamics precisely match those of single-trace TTbar-deformed CFTs at finite temperature, including a critical deformation value $\lambda_c$ where the ground state remains real. The study also connects TsT backgrounds to known marginal/current-current deformations and demonstrates how the Horne–Horowitz and Giveon–Itzhaki–Kutasov solutions fit within the same TTbar framework, highlighting a unified holographic picture for TTbar-type deformations in AdS$_3$/CFT$_2$.

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 $T\bar{T}$, $J\bar{T}$, $T\bar{J}$, and $J\bar{J}$ deformations of 2d CFTs. Applying a TsT transformation to string theory on BTZ $\times S^3\times M^4$ 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 $T\bar{T}$-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 $T\bar{T}$-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 $T\bar{T}$ deformations.