Vertex operator approach for form factors of Belavin's $(Z/nZ)$-symmetric model

TL;DR

This paper develops a vertex operator approach to derive integral formulas for form factors of local operators in Belavin's $(bZ/nbZ)$-symmetric model, utilizing bosonization and vertex-face transformations.

Contribution

It introduces a new vertex operator framework for calculating form factors in the $(bZ/nbZ)$-symmetric model, extending bosonization techniques.

Findings

Constructed free field representations of nonlocal tail operators.

Derived integral formulas for form factors of local operators.

Provided a systematic method applicable to off-diagonal matrix elements.

Abstract

Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. Free field representations of nonlocal tail operators are constructed for off diagonal matrix elements with respect to the ground state sectors. As a result, integral formulae for form factors of any local operators in the $(\mathbb{Z}/n\mathbb{Z})$-symmetric model can be obtained, in principle.