Aspects of the Homogeneous Sine-Gordon models

TL;DR

This paper investigates the mass scales of Homogeneous Sine-Gordon models using thermodynamic Bethe ansatz, confirming the existence of unstable particles at various parameters, thus enhancing understanding of their finite-size effects.

Contribution

It provides a detailed analysis of the mass scales and unstable particle states in Homogeneous Sine-Gordon models through finite-size effect studies.

Findings

Confirmation of unstable particle states at generic parameter values.

Identification of mass scales related to stable and unstable particles.

Validation of semiclassical predictions at large $k$.

Abstract

The physical mass scales that determine the behaviour of general (simply-laced) Homogeneous Sine-Gordon models are investigated by means of a study of their finite-size effects, using the thermodynamic Bethe ansatz. These models describe integrable multiparameter perturbations of the theory of level-$k$ $G$-parafermions, where $G$ is a Lie group. The parameters can be related to adjustable mass scales of stable and unstable particles. Our results confirm the presence of unstable particle states at generic values of $k$, as predicted at large $k$ by semiclassical arguments.