Form factors, KdV and Deformed Hyperelliptic Curves

TL;DR

This paper explores the connection between form factors in integrable quantum field theory and deformations of hyperelliptic curves, revealing new insights into the KdV hierarchy and null vectors through geometric deformations.

Contribution

It introduces a novel geometric deformation framework linking form factors and hyperelliptic curves, advancing understanding of integrable models and the KdV hierarchy.

Findings

Deformation of Riemann bilinear identity relates to form factors.

Null vectors are characterized via geometric deformations.

Provides a new geometric perspective on the KdV hierarchy.

Abstract

We review and summarize recent works on the relation between form factors in integrable quantum field theory and deformation of geometrical data associated to hyper-elliptic curves. This relation, which is based on a deformation of the Riemann bilinear identity, in particular leads to the notion of null vectors in integrable field theory and to a new description of the KdV hierarchy.