Scaling limit of the six vertex model in the framework of free field representation

TL;DR

This paper investigates the scaling limit of the six vertex model, revealing its spectrum, S-matrix, and form factors, and connects these findings to the sine-Gordon model through free field representation.

Contribution

It provides the first detailed analysis of the scaling limit of the six vertex model's spectrum and form factors within the free field framework, linking lattice models to continuum quantum field theories.

Findings

Spectrum and S-matrix of the six vertex model in the scaling limit are characterized.

Form factors match those of the sine-Gordon model at critical coupling.

The structure of free field representation is explained from the lattice model perspective.

Abstract

The scaling limit of the spectrum, $S$ matrix, and of the form factors of the polarization operator in the six vertex model has been found. The result for the form factors is consistent with the form factors of the sine-Gordon model found recently by Lukyanov. We discuss the origin of the structure of the free field representation for the sine-Gordon model at the critical coupling from the point of view of the lattice model.