Virasoro representations and fusion for general augmented minimal models

TL;DR

This paper provides explicit fusion rules and representation structures for augmented logarithmic conformal models, including new higher rank indecomposable representations, and conjectures general fusion rules for broader classes.

Contribution

It introduces the first explicit examples of rank 3 indecomposable representations and proposes general fusion rules for augmented c_{p,q} models.

Findings

Explicit fusion rules for augmented c_{2,3} and c_{2,5} models.

First examples of rank 3 indecomposable representations.

Conjectured general fusion rules for augmented c_{p,q} models.

Abstract

In this paper we present explicit results for the fusion of irreducible and higher rank representations in two logarithmically conformal models, the augmented c_{2,3} = 0 model as well as the augmented Yang-Lee model at c_{2,5} = -22/5. We analyse their spectrum of representations which is consistent with the symmetry and associativity of the fusion algebra. We also describe the first few higher rank representations in detail. In particular, we present the first examples of consistent rank 3 indecomposable representations and describe their embedding structure. Knowing these two generic models we also conjecture the general representation content and fusion rules for general augmented c_{p,q} models.