Resurgence and semiclassical expansion in two-dimensional large-N sigma models

Abstract

Abstract The resurgence structure of the 2d O(N) sigma model at large N is studied with a focus on an IR momentum cutoff scale a that regularizes IR singularities in the semiclassical expansion. Transseries expressions for condensates and correlators are derived as series of the dynamical scale Λ (nonperturbative exponential) and coupling λμ renormalized at the momentum scale μ. While there is no ambiguity when a > Λ, we find for a < Λ that the nonperturbative sectors have new imaginary ambiguities besides the well-known renormalon ambiguity in the perturbative sector. These ambiguities arise as a result of an analytic continuation of transseries coefficients to small values of the IR cutoff a below the dynamical scale Λ. We find that the imaginary ambiguities are cancelled each other when we take all of them into account. By comparing the semiclassical expansion with the transseries for the exact large-N result, we find that some ambiguities vanish in the a → 0 limit and hence the resurgence structure changes when going from the semiclassical expansion to the exact result with no IR cutoff. An application of our approach to the ℂPN−1 sigma model is also discussed. We find in the compactified model with the ℤN twisted boundary condition that the resurgence structure changes discontinuously as the compactification radius is varied.