Hidden Grassmann structure in the XXZ model V: sine-Gordon model

TL;DR

This paper develops a fermionic framework to compute one-point functions in the sine-Gordon model on a cylinder, connecting primary fields through novel fermions and expressing results via thermodynamic Bethe Ansatz data.

Contribution

It introduces a new fermionic description linking primary fields in the sine-Gordon model and expresses one-point functions using a single function derived from Bethe Ansatz equations.

Findings

Fermionic description of primary fields established

One-point functions expressed via Bethe Ansatz data

Connection between different primary fields via new fermions

Abstract

We study one-point functions of the sine-Gordon model on a cylinder. Our approach is based on a fermionic description of the space of descendent fields, developed in our previous works for conformal field theory and the sine-Gordon model on the plane. In the present paper we make an essential addition by giving a connection between various primary fields in terms of yet another kind of fermions. The one-point functions of primary fields and descendants are expressed in terms of a single function defined via the data from the thermodynamic Bethe Ansatz equations.