Fusion Rules of the ${\cal W}_{p,q}$ Triplet Models

Details Fusion Rules of the ${\cal W}_{p,q}$ Triplet Models Fusion Rules of the ${\cal W}_{p,q}$ Triplet Models

2009-07-26

arxiv.org/abs/0907.4421v2

J.Phys.A43:045212,2010

Physics

High Energy Physics

High Energy Physics - Theory

24 pages; v2: Minor expansion of the "Note Added". Version to appear in J. Phys. A

Scientific paper

10.1088/1751-8113/43/4/045212

In this paper we determine the fusion rules of the logarithmic ${\calW}_{p,q}$ 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 ${\cal W}_{2,3}$ model generalises naturally to arbitrary (p,q).

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