Symplectic fusion rings and their metric

TL;DR

This paper investigates the fusion rings of WZW models based on symplectic groups, showing they derive from potentials, and explores their perturbations, metrics, and integrability properties.

Contribution

It demonstrates that symplectic WZW fusion rings originate from specific potentials and analyzes their perturbations, metrics, and integrability, extending understanding of these models.

Findings

Fusion rings arise from described potentials.

Metrics are solutions to the sinh--gordon equation.

Theories exhibit kink structures and are argued to be integrable.

Abstract

The fusion of fields in a rational conformal field theory gives rise to a ring structure which has a very particular form. All such rings studied so far were shown to arise from some potentials. In this paper the fusion rings of the WZW models based on the symplectic group are studied. It is shown that they indeed arise from potentials which are described. These potentials give rise to new massive perturbations of superconformal hermitian symmetric models. The metric of the perturbation is computed and is shown to be given by solutions of the sinh--gordon equation. The kink structure of the theories is described, and it is argued that these field theories are integrable. The $S$ matrices for the fusion theories are argued to be non--minimal extensions of the $G_k\times G_1/ G_{k+1}$ $S$ matrices with the adjoint perturbation, in the case of $G=SU(N)$.