Topological Landau-Ginzburg Matter from Sp(N)_{K} Fusion Rings

TL;DR

This paper constructs and analyzes Landau-Ginzburg potentials that exactly reproduce the fusion rings of Sp(N)_{K} WZW models, revealing their relation to SU(N+1)_{K} potentials and deriving associated topological theories.

Contribution

It introduces explicit Landau-Ginzburg potentials for Sp(N)_{K} fusion rings and explores their relations to SU(N+1)_{K} potentials and topological Landau-Ginzburg theories.

Findings

Fusion rings are realized as critical points of specific potentials.

Sp(N)_{K} and Sp(K)_{N} theories are shown to be identical.

Relations between Sp and SU Landau-Ginzburg models are established.

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 quasi-homogeneous part of the potential associated with Sp(N)_{K} is the same as the quasi-homogeneous 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.