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

Abstract

We study the UV dynamics of $\hat{I}¼T\bar{T}$ deformed conformal field theories formulated as a deformation of generating functions. We explore the issue of non-perturbative completion of the $\hat{I}¼$ 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.

11 pages, 2 figures