Form-Factor Bootstrap and the Operator Content of Perturbed Minimal Models

TL;DR

This paper uses the form-factor bootstrap method to classify the operator content of perturbed minimal models, showing they contain the same number of primary fields as their conformal counterparts and constructing explicit solutions.

Contribution

It applies the form-factor bootstrap to perturbed minimal models to classify operators and explicitly construct solutions corresponding to off-critical primary fields.

Findings

Perturbed models contain the same number of primary fields as conformal models.

Explicit solutions for off-critical primary fields are constructed.

The S-matrix is purely elastic with n massive scalar particles.

Abstract

The form-factor bootstrap approach is applied to the perturbed minimal models $M_{2,2n+3}$ in the direction of the primary field $\phi_{1,3}$. These theories are integrable and contain $n$ massive scalar particles, whose $S$--matrix is purely elastic. The form-factor equations do not refer to a specific operator. We use this fact to classify the operator content of these models. We show that the perturbed models contain the same number of primary fields as the conformal ones. Explicit solutions are constructed and conjectured to correspond to the off-critical primary fields $\phi_{1,k}$.