Form factor perturbation theory from finite volume

TL;DR

This paper introduces a finite volume regularization method to extend form factor perturbation theory to higher orders in nonintegrable models, demonstrated on double sine-Gordon theory with results matching other approaches.

Contribution

A novel finite volume regularization approach enabling higher-order form factor perturbation calculations in nonintegrable models.

Findings

Vacuum energy density correction computed at second order.

Breather mass correction evaluated at second order.

Results agree with truncated conformal space approach.

Abstract

Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in form factor perturbation theory and in principle works to any order. The procedure is carried out in detail for double sine-Gordon theory, where the vacuum energy density and breather mass correction is evaluated at second order. The results agree with those obtained from the truncated conformal space approach. The regularization procedure can also be used to compute other spectral sums involving disconnected pieces of form factors such as those that occur e.g. in finite temperature correlators.