Comments on single trace $T\bar{T}$ and other current-current deformations

TL;DR

This paper analyzes a solvable irrelevant deformation of string theory on AdS3, exploring its geometric, spectral, and correlation properties, and discusses extending such deformations to other conformal models.

Contribution

It provides a detailed study of the $J^-ar{J}^-$ deformation in AdS3 string theory, including geometry, spectrum, and correlation functions, and explores generalizations to other models.

Findings

The deformed background interpolates between AdS3 and flat spacetime with a Hagedorn spectrum.

Correlation functions and spectra are explicitly computed for the deformed worldsheet theory.

The deformation can be extended to other conformal models beyond AdS3.

Abstract

String theory on AdS$_3$ with NS-NS fluxes admits a solvable irrelevant deformation which is close to the $T\bar{T}$ deformation of the dual CFT$_2$. This consists of deforming the worldsheet action, namely the action of the $SL(2,\mathbb{R})$ WZW model, by adding to it the operator $J^-\bar{J}^-$, constructed with two Kac-Moody currents. The geometrical interpretation of the resulting theory is that of strings on a conformally flat background that interpolates between AdS$_3$ in the IR and a flat linear dilaton spacetime with Hagedorn spectrum in the UV, having passed through a transition region of positive curvature. Here, we study the properties of this string background both from the point of view of the low-energy effective theory and of the worldsheet CFT. We first study the geometrical properties of the semiclassical geometry, then we revise the computation of correlation functions and of the spectrum of the $J^-\bar{J}^-$-deformed worldsheet theory, and finally we discuss how to extend this type of current-current deformation to other conformal models.