Integrability of Bukhvostov-Lipatov model and ODE/IQFT correspondence

Abstract

We consider Bukhvostov-Lipatov model, an integrable quantum field theory in two dimensions that arises as an approximation to O(3) NLSM. We compute its vacuum energy on a cylinder with twisted boundary conditions in weak coupling limit using renormalized perturbation theory, and in the short distance limit using conformal perturbation theory. The exact solution of this model via coordinate Bethe ansatz is provided. Two different regularizations of Bethe ansatz equations are constructed. The vacuum state is constructed and the vacuum energy is computed within both regularizations using numerical methods. Bethe ansatz equations governing the vacuum state are shown to coincide with functional relations between connection coefficients of auxiliary linear problem for an integrable classical PDE known as modified sinh-Gordon equation. Based on this correspondence the system of nonlinear integral equations equivalent to the full system of Bethe ansatz equations is derived for massive and conformal cases. This system of NLIE was solved numerically. We have also used it to investigate analytically the properties of solution describing vacuum state. Finally, we have derived a formula that expresses the vacuum energy of Bukhvostov-Lipatov model in terms of the regularized area of constant mean curvature surface embedded into ADS3 space. Show more