On the spectrum of the Sinh-Gordon model in finite volume

TL;DR

This paper characterizes the spectrum of the Sinh-Gordon model in finite volume using nonlinear integral equations, providing evidence that these solutions describe the model's spectrum across different energy limits.

Contribution

It introduces a new integral equation framework to describe the Sinh-Gordon spectrum and demonstrates its validity in both infrared and ultraviolet regimes.

Findings

Solutions connect infrared and ultraviolet limits

Evidence links solutions to Liouville theory

Spectrum characterized by nonlinear integral equations

Abstract

We derive a characterization of the spectrum of the Sinh-Gordon model in terms of certain nonlinear integral equations. There exists a large class of solutions to these equations which allows a continuation between the infrared and the ultraviolet limits, respectively. We present nontrivial evidence for the claim that the class of solutions in question describes the spectrum of the Sinh-Gordon model completely in both of these limits. The evidence includes some nontrivial relations to Liouville theory.