Resurgent properties of $T\overline{T}$-deformed conformal field theories

Abstract

We elaborate on the resurgence analysis on the $T\overline{T}$-deformed 2d conformal field theory (CFT). Writing the deformed partition function as an infinite series in the deformation parameter $\lambda$, we develop efficient analytical methods to compute high-order terms of the $\lambda$-series. Based on the asymptotic behavior of the large-order perturbative series, we show that the $\lambda$-series is asymptotic and extract non-perturabtive contributions by resurgence. This paper extends a previous Letter of the same authors to interacting rational CFTs, with Lee-Yang CFT as a concrete example. We also discuss possible implications of the resurgence results on holography.