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

Understand

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).