On the Structure of the Fusion Ideal

TL;DR

This paper establishes a finite bound on the relations defining fusion rings of positive energy loop group representations and explicitly computes the fusion ring for the G2 Lie group at all levels.

Contribution

It proves a universal bound on the relations of fusion rings and provides explicit calculations for G2, advancing understanding of fusion algebra structures.

Findings

Finite level-independent bound on fusion relations

Explicit fusion ring computation for G2 at all levels

Enhanced understanding of fusion algebra structures

Abstract

We prove that there is a finite level-independent bound on the number of relations defining the fusion ring of positive energy representations of the loop group of a simple, simply connected Lie group. As an illustration, we compute the fusion ring of $G_2$ at all levels.