Ward Identities and Integrable Differential Equations in the Ising Field Theory

TL;DR

This paper demonstrates how Ward Identities linked to local Integrals of Motion lead to Painleve equations for Ising correlation functions and derives matrix elements relevant for mass corrections in perturbed Ising models.

Contribution

It provides a simple derivation of Painleve equations from Ward Identities and applies these to compute matrix elements and mass corrections in the Ising field theory.

Findings

Painleve equations follow from Ward Identities in Ising theory

Derived matrix elements of spin operators between particle states

Evaluated leading mass corrections in magnetic field perturbation

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 $\sigma(x)\sigma(x')$ 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.