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

TL;DR

The paper extends a solvable $T\bar{T}$-like deformation of AdS$_3$/CFT$_2$ to the presence of a conformal boundary, formulating the bulk and boundary actions and examining disc observables. By computing the bulk 1-point, boundary-boundary 2-point, and bulk-boundary 2-point functions, the authors extract anomalous dimensions $\delta h_{\Phi}^p = 2\lambda_0 |p|^2$ and $\delta h_{\Psi}^\nu = 2\lambda_0 \nu^2$, and show exact agreement with corresponding sphere results, up to regularization scheme subtleties. They perform cross-checks using multiple regularization methods and a perturbative Coulomb gas approach, confirming the consistency of the deformation across bulk and boundary sectors. The results illuminate how a single-trace, solvable deformation propagates to boundary observables and provide a controlled framework for non-AdS holography with a UV Hagedorn spectrum.

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.