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 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.

13 pages

References in corpus (2)

• Topological Matter, Integrable Models and Fusion Rings
• Fusion Potentials for G_k and Handle Squashing

Cited by in corpus (14)

• A New Supersymmetric Index
• The Verlinde Algebra And The Cohomology Of The Grassmannian
• Fusion rules in conformal field theory
• D-branes on group manifolds and fusion rings
• Generalized Fusion Potentials
• Presentations of Wess-Zumino-Witten Fusion Rings
• Fusion Potentials for G_k and Handle Squashing
• Fusion potentials I
• Bulk perturbations of N=2 branes
• Level-rank duality of D-branes on the SU(N) group manifold
• Level-rank duality of untwisted and twisted D-branes
• Integrable N = 2 Landau-Ginzburg Theories from Quotients of Fusion Rings
• $K$-theory of AF-algebras from braided C*-tensor categories
• BF Theories and Group-Level Duality