$T\bar{T}$ type deformation in the presence of a boundary

TL;DR

This paper investigates a solvable deformation of AdS$_3$/CFT$_2$ with a boundary, deriving exact results for operator dimensions and correlation functions, and analyzing regularization schemes to ensure consistency.

Contribution

It provides a detailed analysis of the deformed worldsheet theory with a boundary, including explicit formulas for correlators and anomalous dimensions, and compares different regularization methods.

Findings

Exact expression for bulk primary operator expectation value on the disc

Agreement between different computational approaches for anomalous dimensions

Reproduction of boundary and bulk operator anomalous dimensions

Abstract

We continue the study of a recently proposed solvable irrelevant deformation of an AdS$_3$/CFT$_2$ correspondence that leads in the UV to a theory with Hagedorn spectrum. This can be thought of as a single trace analog of the $T\bar{T}$-deformation of the dual CFT$_2$. Here we focus on the deformed worldsheet theory in presence of a conformal boundary. First, we compute the expectation value of a bulk primary operator on the disc geometry. We give a closed expression for such observable, from which we obtain the anomalous conformal dimension induced by the deformation. We compare the result with that coming from the computation of the 2-point correlation function on the sphere, finding exact agreement. We perform the computation using different techniques and making a comparative analysis of different regularization schemes to solve the logarithmically divergent integrals. This enables us to perform further consistency checks of our result by computing other observables of the deformed theory: We compute both the bulk-boundary 2-point and the boundary-boundary 2-point functions and are able to reproduce the anomalous dimensions of both boundary and bulk operators.