Expectation values of local fields for a two-parameter family of integrable models and related perturbed conformal field theories

TL;DR

The paper develops an exact framework for vacuum expectation values in a two-parameter family of integrable QFTs introduced by Fateev, via reflection relations and Coulomb gas techniques, and expresses VEVs in terms of a universal function $G(a,b,c)$. It demonstrates how these VEVs encode observables in perturbed CFTs, enabling explicit results for parafermionic sine-Gordon theories and for integrable perturbed SU(2) coset models, with consistency checks across sine-Gordon, SUSY extensions, and large-$n$ limits. The authors also derive exact three-point functions and residue relations that reproduce perturbative expansions, and show how analytic continuation connects to parafermionic sinh-Gordon theories. Overall, the work provides a comprehensive, exact bridge between local-field VEVs in massive integrable QFTs and correlators in their perturbed CFT descriptions, with broad applications to parafermionic and coset models.

Abstract

We calculate the vacuum expectation values of local fields for the two-parameter family of integrable field theories introduced and studied by Fateev. Using this result we propose an explicit expression for the vacuum expectation values of local operators in parafermionic sine-Gordon models and in integrable perturbed SU(2) coset conformal field theories.