Thermodynamic Bethe ansatz of the homogeneous sine-Gordon models

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 Smatrices 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.

Null-polygonal minimal surfaces in AdS4 from perturbed W minimal models

“…The corresponding relation was also inferred in the same paper between the present n-cusp minimal surfaces in AdS 4 and the SU(n − 4) 4 /U(1) n−5 HSG model. The relation is indeed confirmed by comparing the integral equations in the previous subsection with the TBA equations of this HSG model, which are read off from the general expression in [36]. Let us see this explicitly below.…”

From integrability to conductance, impurity systems

“…The two signs in (3.13) capture the breaking of parity invariance in the limiting case, i.e. the two equations in (3.14) correspond to taking the particle either clockwise or anti-clockwise around the world line as formulated for the parity breaking case for the first time in [43]. We do not expect to recover from here the equations for a purely reflecting boundary which were suggested in [44], since the equations (3.6) and (3.7) do not make sense in the limit T,T → 0.…”

Thermodynamic Bethe Ansatz and Form Factors for the Homogeneous Sine-Gordon Models

“…The work I want to report about [1,2,3,4,5,6] is based on a collaboration with Olalla Castro-Alvaredo (Universidad de Santiago de Compostela), Christian Korff (Stony Brook) and Luis Miramontes (Universidad de Santiago de Compostela).…”

“…Recently we investigated [1,2,3,4,5,6] a class of models, the homogeneous Sine-Gordon model (HSG) [8] and its generalization, for which the bootstrap program was completed to a large extend. In comparison with other models, describable by a well-defined Lagrangian and which have been studied so far in 1+1 dimensions, the HSG-models possess two interesting novel features familiar from realistic 1+3 dimensional theories.…”

“…Due to the limited amount of time and space I will focus in my account on the main findings, referring the reader to the original literature [1,2,3,4,5,6] and [11,12,13] for more details and general background.…”