Ward Identities and Integrable Differential Equations in the Ising Field Theory

Abstract

We show that the celebrated Painleve equations for the Ising correlation functions follow in a simple way from the Ward Identities associated with local Integrals of Motion of the doubled Ising field theory. We use these Ward Identities to derive the equations determining the matrix elements of the product $σ(x)σ(x')$ between any particle states. The result is then applied in evaluating the leading mass corrections in the Ising field theory perturbed by an external magnetic field.