Notes on scaling limits in SOS models, local operators and form factors

TL;DR

This paper investigates the scaling limits of SOS and RSOS models, linking them to sine-Gordon and perturbed minimal models, and derives integral representations for form factors and operator correspondences.

Contribution

It establishes the correspondence between local operators in SOS models and quantum field theory fields, providing integral form factors and connecting vacuum expectations across models.

Findings

Derived integral representations for form factors.

Established correspondence between local operators and quantum fields.

Connected vacuum expectation values in different models.

Abstract

Scaling limits of the SOS and RSOS models in the regime~III are considered. These scaling limits are believed to be described by the sine-Gordon model and the restricted sine-Gordon models (or perturbed minimal conformal models) respectively. We study two different scaling limits and establish the correspondence of the scaling local height operators to exponential or primary fields in quantum field theory. An integral representation for form factors is obtained in this way. In the case of the sine-Gordon model this reproduces Lukyanov's well known representation. The relation between vacuum expectation values of local operators in the sine-Gordon model and perturbed minimal models is also discussed.