Thermodynamic Bethe Ansatz of the Homogeneous Sine-Gordon models

TL;DR

This paper uses the thermodynamic Bethe Ansatz to analyze the high energy behavior of scattering matrices for Homogeneous sine-Gordon models, revealing their connection to coset conformal field theories and the formation of unstable bound states.

Contribution

It provides a detailed analysis of the S-matrix proposal for Homogeneous sine-Gordon models, including numerical results and the identification of flows between conformal cosets.

Findings

Recovery of effective central charge in the ultraviolet regime.

Observation of staircase pattern in the scaling function for models with resonance parameters.

Identification of the ultraviolet-infrared flow between different conformal cosets.

Abstract

We apply the thermodynamic Bethe Ansatz to investigate the high energy behaviour of a class of scattering matrices which have recently been proposed to describe the Homogeneous sine-Gordon models related to simply laced Lie algebras. A characteristic feature is that some elements of the suggested S-matrices are not parity invariant and contain resonance shifts which allow for the formation of unstable bound states. From the Lagrangian point of view these models may be viewed as integrable perturbations of WZNW-coset models and in our analysis we recover indeed in the deep ultraviolet regime the effective central charge related to these cosets, supporting therefore the S-matrix proposal. For the $SU(3)_k$-model we present a detailed numerical analysis of the scaling function which exhibits the well known staircase pattern for theories involving resonance parameters, indicating the energy scales of stable and unstable particles. We demonstrate that, as a consequence of the interplay between the mass scale and the resonance parameter, the ultraviolet limit of the HSG-model may be viewed alternatively as a massless ultraviolet-infrared-flow between different conformal cosets. For $k=2$ we recover as a subsystem the flow between the tricritical Ising and the Ising model.