Form factors of descendant operators in the Bullough-Dodd model

TL;DR

This paper develops a free field representation for descendant operator form factors in the Bullough-Dodd model, confirming their structure, properties, and reflection relations, thus advancing the understanding of integrable quantum field theories.

Contribution

It introduces a modified free field approach for descendant form factors and proves their correspondence with descendant operators, including reflection symmetry properties.

Findings

Number of solutions matches descendant operators in each level.

Form factors exhibit cluster factorization property.

Form factors satisfy reflection relations and possess a reflection invariant basis.

Abstract

We propose a free field representation for the form factors of descendant operators in the Bullough-Dodd model. This construction is a particular modification of Lukyanov's technique for solving the form factors axioms. We prove that the number of proposed solutions in each level subspace of the chiral sectors coincide with the number of the corresponding descendant operators in the Lagrangian formalism. We check that these form factors possess the cluster factorization property. Besides, we propose an alternative free field representation which allows us to study analytic properties of the form factors effectively. In particular, we prove that the form factors satisfy non trivial identities known as the "reflection relations". We show the existence of the reflection invariant basis in the level subspaces for a generic values of the parameters.