Fusion Algebras of Logarithmic Minimal Models

Understand

We present explicit conjectures for the chiral fusion algebras of the logarithmic minimal models LM(p,p') considering Virasoro representations with no enlarged or extended symmetry algebra.

• The generators of fusion are countably infinite in number but the ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of representations decomposes into a finite direct sum of representations.
• The fusion rules are commutative, associative and exhibit an sl(2) structure but require so-called Kac representations which are reducible yet indecomposable representations of rank 1.
• In particular, the identity of the fundamental fusion algebra is in general a reducible yet indecomposable Kac representation of rank 1.