Form Factors, deformed Knizhnik-Zamolodchikov equations and finite-gap integration

TL;DR

This paper explores the connection between form factors in integrable models, affine algebra limits, and finite-gap integration of classical equations, revealing new insights into their mathematical structure.

Contribution

It demonstrates that form factors in certain integrable models satisfy KZ equations at level 0 and links this to finite-gap integration methods.

Findings

Form factors obey KZ equations at level 0.

The algebra of nonlocal charges becomes affine in the limit.

Connection established between quantum form factors and classical finite-gap integration.

Abstract

We study the limit of asymptotically free massive integrable models in which the algebra of nonlocal charges turns into affine algebra. The form factors of fields in that limit are described by KZ equations on level 0. We show the limit to be connected with finite-gap integration of classical integrable equations.