A method to determine the operator content of perturbed conformal field theories

TL;DR

This paper introduces a method based on the form factor bootstrap to determine the operator content of massive integrable quantum field theories, specifically applied to perturbations of the Ising model, revealing a fermionic sum structure.

Contribution

It presents a novel approach to identify the local operator structure in perturbed conformal field theories using form factors and fermionic character representations.

Findings

Operator space factorizes into chiral components as Z=∑ c(q) c( q̄ )

Content of operators expressed via fermionic sum representations of Virasoro characters

Method successfully applied to integrable perturbations of the Ising conformal point

Abstract

A method to determine the full structure of the space of local operators of massive integrable field theories, based on the form factor bootstrap approach is presented. This method is applied to the integrable perturbations of the Ising conformal point. It is found that the content of local operators can be expressed in terms of fermionic sum representations of the characters $\c(q)$ of the Virasoro irreducible representations of the minimal model $\M_{3,4}$. The space of operators factorises into chiral components as $Z=\sum \c(q) \c(\q)$, but with the relation $\q=q^{-1}$.