Topological Matter, Integrable Models and Fusion Rings

TL;DR

This paper demonstrates how topological models and fusion rings can be embedded into perturbed N=2 supersymmetric models, revealing connections between topological matter, integrable systems, and algebraic structures.

Contribution

It introduces a novel embedding of the fusion ring into perturbed topological matter models derived from twisted N=2 coset models, linking topological and integrable field theories.

Findings

Fusion ring embedded as a sub-ring of the chiral primary ring.

Perturbation leads to an integrable N=2 supersymmetric field theory.

Connection established between topological matter models and integrable systems.

Abstract

We show how topological $G_k/G_k$ models can be embedded into the topological matter models that are obtained by perturbing the twisted $N=2$ supersymmetric, hermitian symmetric, coset models. In particular, this leads to an embedding of the fusion ring of $G$ as a sub-ring of the perturbed, chiral primary ring. The perturbation of the twisted $N=2$ model that leads to the fusion ring is also shown to lead to an integrable $N=2$ supersymmetric field theory when the untwisted $N=2$ superconformal field theory is perturbed by the same operator and its hermitian conjugate.