The complete trans-series for conserved charges in integrable field theories

We analyze the vacuum expectation values of conserved charges in two dimensional integrable theories. We study the situations when the ground-state can be described by a single integral equation with a finite support: the thermodynamic limit of the Bethe ansatz equation. We solve this integral equation by expanding around the infinite support limit and write the expectation values in terms of an explicitly calculable trans-series, which includes both perturbative and all non-perturbative corrections. These different types of corrections are interrelated via resurgence relations, which we all reveal. We provide explicit formulas for a wide class of bosonic and fermionic models including the O ( N ) (super) symmetric nonlinear sigma and Gross–Neveu, the S U ( N ) invariant principal chiral and chiral Gross–Neveu models along with the Lieb-Liniger and Gaudin-Yang models and the case of the disk capacitor. With numerical analyses we demonstrate that the laterally Borel resummed trans-series is convergent and reproduces the physical result. • The groundstate energy and other conserved charges can be expressed by a single integral equations with a finite support in many two dimensional integrable theories. • These theories include the O(N) symmetric sigma model, its supersymmetric extension, the O(N) Gross-Neveu model, the SU(N) principal chiral model, the SU(N) chiral Gross-Neveu model, the Lieb-Liniger model, the Gaudin-Yang model and the circular disk capacitor. • The integral equation can be solved in terms of an explicitly calculable transseries. • The perturbative and all the non-perturbative parts of the transseries are interrelated by very simple resurgence relations. • Numerical analysis shows that the laterally Borel resummed trans-series is convergent and reproduces the physical result of the integral equation.