Abstract

We study the solution of the TBA integral equation describing the energy density of finite density states in the 1+1 dimensional O(N) non-linear sigma model by the Wiener-Hopf method. Using Volin’s algorithm we determine the asymptotic series expansion of the energy density in powers of a non-perturbative running coupling to very large orders. We calculate the first 2000 terms of the series for the N=4 case, which allows us to determine the first few alien derivatives of the perturbative series. We show that (at least in this case) resurgence theory works in its strongest version: the physical resummation of the perturbative series is given by the median resummation and this agrees with the result of the original exact TBA equation. For the O(3) case we calculate the 1- and 2-instanton contributions perturbatively to very large orders.