Finite size effects and the supersymmetric sine-Gordon models

TL;DR

This paper develops nonlinear integral equations to analyze the groundstate energies of various supersymmetric sine-Gordon models, including N=1 and N=2 cases, and their relation to certain perturbed conformal field theories.

Contribution

It introduces a unified set of nonlinear integral equations for multiple supersymmetric sine-Gordon models and their perturbations, extending previous analytical methods.

Findings

Derived equations describe groundstate energies of N=1 and N=2 supersymmetric sine-Gordon models.

Connected the models to specific perturbed conformal field theories at rational levels.

Provided a framework for analyzing finite size effects in these models.

Abstract

We propose nonlinear integral equations to describe the groundstate energy of the fractional supersymmetric sine-Gordon models. The equations encompass the N=1 supersymmetric sine-Gordon model as well as the phi_(id,id,adj) perturbation of the SU(2)_L x SU(2)_K /SU(2)_(L+K) models at rational level K. A second set of equations are proposed for the groundstate energy of the N=2 supersymmetric sine-Gordon model.