Topological matter, integrable models and fusion rings

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.