TOPOLOGICAL LANDAU-GINZBURG MATTER FROM SP(N)K FUSION RINGS

Abstract

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 associated with SP (N)K is the same as the quasihomogeneous part of that associated with SU (N+1)K, showing that these potentials are different perturbations of the same Grassmannian potential. Twisted N=2 topological Landau-Ginzburg theories are derived from these superpotentials. The correlation functions, which are just the SP (N)K Verlinde dimensions, are expressed as fusion residues. We note that the SP (N)K and SP (K)N topological Landau-Ginzburg theories are identical, and that while the SU (N)K and SU (K)N topological Landau-Ginzburg models are not, they are simply related.