Abstract

We discuss the resurgent structure of quantum field theory, with emphasis on IR-renormalon and phase transition. We study the 2D sigma models at large N, with an IR momentum cutoff scale A introduced to regularize IR singularities in the trans-series expression. Trans-series expressions for physical quantities are derived as series of the dynamical scale \Lambda and coupling \lambda. While there is no ambiguity when A > \Lambda, we find for A < \Lambda that the nonperturbative sectors have new imaginary ambiguities besides the well-known renormalon ambiguity in the perturbative sector, which arise as a result of an analytic continuation of trans-series coefficients to A < \Lambda. We show that the renormalon imaginary ambiguity is cancelled by the combined imaginary ambiguities at the different orders of \Lambda in the trans-series. We find in the compactified model with the ZN twisted boundary condition that the resurgence structure changes discontinuously as the compactification radius is varied. We also discuss the nontrivial relation between the order of phase transition and the behavior of Borel singularities.