Indecomposable Fusion Products

TL;DR

This paper introduces a new algorithm to analyze indecomposable fusion products of Virasoro algebra representations at specific central charges, revealing novel structures and their closure properties.

Contribution

The paper presents a novel algorithm for studying fusion products level by level and characterizes new indecomposable Virasoro representations at c=-2 and c=-7.

Findings

Identification of indecomposable Virasoro modules

Algorithm for fusion analysis at each level

Closure of extended representation set under fusion

Abstract

We analyse the fusion products of certain representations of the Virasoro algebra for c=-2 and c=-7 which are not completely reducible. We introduce a new algorithm which allows us to study the fusion product level by level, and we use this algorithm to analyse the indecomposable components of these fusion products. They form novel representations of the Virasoro algebra which we describe in detail. We also show that a suitably extended set of representations closes under fusion, and indicate how our results generalise to all (1,q) models.