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

TL;DR

This paper explores a solvable $T\bar{T}$-deformation of AdS$_3$/CFT$_2$, analyzing its impact on correlation functions, operator dimensions, and the spectrum, revealing a transition from AdS$_3$ to a linear dilaton background.

Contribution

It explicitly computes the anomalous dimensions of operators under the $T\bar{T}$ deformation and analyzes the resulting correlation functions within the holographic framework.

Findings

Deformation leads to a logarithmic divergence in correlation functions.

Operators acquire anomalous dimensions due to the deformation.

The spectrum interpolates between AdS$_3$ and a linear dilaton background.

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 $\sigma $-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS$_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.