On form factors and Macdonald polynomials

TL;DR

This paper explores the algebraic construction of form factors in sinh-Gordon theory, revealing that null vectors correspond to degenerate Macdonald polynomials with specific parameters, and provides integral representations for these vectors.

Contribution

It establishes a novel connection between null vectors in sinh-Gordon form factors and degenerate Macdonald polynomials with rectangular partitions and specific parameters.

Findings

Null vectors correspond to degenerate Macdonald polynomials with t=-q.

An integral representation for null vectors is derived.

Applications of the integral representation are discussed.

Abstract

We are developing the algebraic construction for form factors of local operators in the sinh-Gordon theory proposed in [B.Feigin, M.Lashkeivch, 2008]. We show that the operators corresponding to the null vectors in this construction are given by the degenerate Macdonald polynomials with rectangular partitions and the parameters $t=-q$ on the unit circle. We obtain an integral representation for the null vectors and discuss its simple applications.