Analytic resurgence in the O(4) model

A bstract We study the perturbative expansion of ground state energy in presence an external field coupled to a conserved charge integrable two-dimensional O(4) nonlinear sigma model. By solving Volin’s algebraic equations for coefficients we large order asymptotic behaviour series analytically. confirm previously numerically found leading and nearest singularities Borel transformed associated alien derivatives. find “resurgence” behaviour: derivatives can be expressed terms original series. simplified ‘toy’ model is also considered: here closed form resurgence properties are very similar that real problem.