We discuss when and how the Verlinde dimensions of a rational conformal field theory can be expressed as correlation functions in a topological LG theory. It is seen that a necessary condition is that the RCFT fusion rules must exhibit an extra symmetry. We consider two particular perturbations of the Grassmannian superpotentials. The topological LG residues in one perturbation, introduced by Gepner, are shown to be a twisted version of the SU (N) k Verlinde dimensions. The residues in the… Expand

Using Chern–Simons gauge theory, we show that the fusion ring of the conformal field theory Gk (G any Lie algebra) is isomorphic to P [u] (∇V ) where V is a polynomial in u and (∇V ) is the ideal… Expand

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling… Expand

We find and analyze the Landau-Ginzburg potentials whose critical points determine chiral rings which are exactly the fusion rings of SP(N)K WZW models. The quasihomogeneous part of the potential… Expand

It is shown how coupling to gauge fields can be used to explain the basic facts concerning holomorphic factorization of the WZW model of two dimensional conformal field theory, which previously have… Expand

The algebraic structure of fusion rings in rational conformal field theories is analyzed in detail in this paper. A formalism which closely parallels classical tools in the study of the cohomology of… Expand