Thermodynamic Bethe Ansatz of the Homogeneous Sine-Gordon models

Details Thermodynamic Bethe Ansatz of the Homogeneous Sine-Gordon models Thermodynamic Bethe Ansatz of the Homogeneous Sine-Gordon models

1999-12-21

arxiv.org/abs/hep-th/9912196v1

Nucl.Phys. B575 (2000) 535-560

Physics

High Energy Physics

High Energy Physics - Theory

30 pages Latex, two figures

Scientific paper

10.1016/S0550-3213(00)00162-0

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.

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