Fixed points and fusion rings. Part 1

TL;DR

This paper develops fixed point factorisation formulas for fusion rings of WZW models beyond SU(n), generalizing previous results and setting the stage for future applications in conformal field theory and related areas.

Contribution

It generalizes fixed point factorisation formulas from SU(n) to other classical algebras, expanding the understanding of fusion rings in WZW models.

Findings

Derived fixed point factorisation formulas for classical algebras

Connected fixed point data with twining characters

Laid groundwork for future fusion ring applications

Abstract

In the first of this two-part series, we find `fixed point factorisation' formulas, towards an understanding of the fusion ring of WZW models. Fixed-point factorisation refers to the simplifications in the data of a CFT involving primary fields fixed by simple-currents. Until now, it has been worked out only for SU(n), where it has developed into a powerful tool for understanding the fusion rings of WZW models of CFT -- e.g. it has lead to closed formulas for NIM-reps and D-brane charges and charge-groups. In this paper, we generalise these formulas to the other classical algebras, laying the groundwork for future applications to fusion rings (Part 2). We also discuss connections with the twining characters of Fuchs-Schellekens-Schweigert.