Fusion Potentials for G_k and Handle Squashing

Abstract

Using Chern-Simons gauge theory, we show that the fusion ring of the conformal field theory G_k is isomorphic to P(u)/(\del V), where V is a polynomial in u and (\del V) is the ideal generated by the conditions \del V=0. We also derive a residue-like formula for the correlation functions in the Chern-Simons theory thus providing a RCFT version of the residue formula for the TLG models. An operator that acts like the measure in the residue formula has the ionterpretation of a handle squashing operator and an explicit formula for this operator is given.

(24 pages)

References in corpus (2)

• Topological Matter, Integrable Models and Fusion Rings
• Topological Landau-Ginzburg Matter from Sp(N)_{K} Fusion Rings

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• Integrable N = 2 Landau-Ginzburg Theories from Quotients of Fusion Rings
• A Kac-Weyl Character Identity