Integrable quantum field theory with boundaries: the exact g-function

TL;DR

This paper develops an exact integral equation for the g-function in boundary quantum field theories using a cluster expansion approach, providing a new infrared expansion formula applicable to models with diagonal scattering.

Contribution

It introduces a novel method using an n-particle cluster expansion to derive an exact infrared expansion for the g-function in off-critical boundary quantum field theories.

Findings

Derived an exact infrared expansion for the g-function in integrable models.

Proposed a general formula for the g-function valid for models with diagonal scattering.

Validated the approach with the thermally-perturbed Ising and Lee-Yang models.

Abstract

The g-function was introduced by Affleck and Ludwig in the context of critical quantum systems with boundaries. In the framework of the thermodynamic Bethe ansatz (TBA) method for relativistic scattering theories, all attempts to write an exact integral equation for the off-critical version of this quantity have, up to now, been unsuccesful. We tackle this problem by using an n-particle cluster expansion, close in spirit to form-factor calculations of correlators on the plane. The leading contribution already disagrees with all previous proposals, but a study of this and subsequent terms allows us to deduce an exact infrared expansion for g, written purely in terms of TBA pseudoenergies. Although we only treat the thermally-perturbed Ising and the scaling Lee-Yang models in detail, we propose a general formula for g which should be valid for any model with entirely diagonal scattering.