Algebraic approach to form factors in the complex sinh-Gordon theory

TL;DR

This paper develops an algebraic method to compute form factors in the complex sinh-Gordon theory, linking it to known models and proposing a new approach for descendant operators.

Contribution

It introduces an algebraic framework for form factors in the complex sinh-Gordon theory, including generating functions and properties like cluster factorization.

Findings

Form factors for exponential fields derived from $Z_N$-symmetric Ising model

Proposed an Ansatz for descendant operators' form factors

Established properties such as cluster factorization and reflection equations

Abstract

We study form factors of the quantum complex sinh-Gordon theory in the algebraic approach. In the case of exponential fields the form factors can be obtained from the known form factors of the $Z_N$-symmetric Ising model. The algebraic construction also provides an Ansatz for form factors of descendant operators. We obtain generating functions of such form factors and establish their main properties: the cluster factorization and reflection equations.