Fusion Rules of the \(\mathcal{W}_{p,q}\) Triplet Models

Extends the analysis of the central charge zero triplet model to the whole family of logarithmic \(\mathcal{W}_{p,q}\) triplet models, proposing associative fusion rules and identifying the projective covers. It also determines where fusion gives a consistent product on the Grothendieck group and suggests a candidate modular invariant partition function.

Abstract

In this paper we determine the fusion rules of the logarithmic \(\mathcal{W}_{p,q}\) triplet theory and construct the Grothendieck group with subgroups for which consistent product structures can be defined. The fusion rules are then used to determine projective covers. This allows us also to write down a candidate for a modular invariant partition function. Our results demonstrate that recent work on the \(\mathcal{W}_{2,3}\) model generalises naturally to arbitrary (p,q).

Recommended citation: S. Wood, J. Phys. A 43, 045212 (2010)
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