On the Operator Content of the Sinh-Gordon Model

TL;DR

This paper classifies the operator content of the Sinh-Gordon model using form-factor bootstrap equations, identifying solutions with specific operators and providing explicit form factors for key fields.

Contribution

It introduces a systematic classification of local operators in the Sinh-Gordon model and derives explicit form factors for fundamental operators.

Findings

Operator space organized into a tower structure

Identification of solutions with exponential operators

Explicit form factors for  and 

Abstract

We classify the operator content of local hermitian scalar operators in the Sinh-Gordon model by means of independent solutions of the form-factor bootstrap equations. The corresponding linear space is organized into a tower-like structure of dimension $n$ for the form factors $F_{2n}$ and $F_{2n-1}$. Analyzing the cluster property of the form factors, a particular class of these solutions can be identified with the matrix elements of the operators $e^{k g\phi}$. We also present the complete expression of the form factors of the elementary field $\phi(x)$ and the trace of the energy-momentum tensor $\Theta(x)$.