$T\bar{T}$-deformations, AdS/CFT and correlation functions

TL;DR

The paper presents a solvable irrelevant deformation of AdS$_3$/CFT$_2$ generated by a single-trace operator, yielding a bulk background that flows from AdS$_3$ in the IR to a linear-dilaton (little string theory) regime in the UV. By exploiting the Wakimoto representation of the $SL(2,\mathbb{R})$ WZW model, the authors compute exact worldsheet 2-point functions and reveal an operator anomalous dimension $\Delta=\Delta_0+4\lambda_0|p|^2$ with $\Delta_0=\frac{h(1-h)}{k}$, arising from a logarithmic divergence in the deformation. They verify the spectrum against a coset construction, and extend the analysis to higher-point functions, which can be expressed through Liouville theory correlators, highlighting the solvable structure and providing explicit forms for correlators and spectrum. The work clarifies the holographic interpretation of the deformation, connects to Liouville and coset frameworks, and suggests avenues for exploring related integrable deformations and non-local UV behavior in holography.

Abstract

A solvable irrelevant deformation of AdS$_3$/CFT$_2$ 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 $T\bar{T}$ 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 AdS$_3$ 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.