Comments on $T \bar T$ double trace deformations and boundary conditions

TL;DR

This paper investigates the UV behavior of $ ext{T}ar{ ext{T}}$ deformed conformal field theories, proposing a non-perturbative integral formulation and highlighting the significance of boundary conditions at the cutoff surface.

Contribution

It introduces an integral expression for the $ ext{T}ar{ ext{T}}$ deformation's non-perturbative completion and emphasizes the preference for Neumann boundary conditions over Dirichlet.

Findings

Neumann boundary conditions are more natural for the metric at the cutoff surface.

An integral expression for the deformation's non-perturbative completion is derived.

Connections to boundary conformal field theories are discussed.

Abstract

We study the UV dynamics of $\mu T \bar T$ deformed conformal field theories formulated as a deformation of generating functions. We explore the issue of non-perturbative completion of the $\mu$ expansion by deriving an integral expression using the Fourier/Legendre transform technique, and show that it is more natural to impose Neumann, as opposed to the Dirichlet, boundary condition, for the metric at the cut-off surface recently proposed by McGough, Mezei, and Verlinde. We also comment on interesting connection to boundary conformal field theories.