Fixed points and fusion rings. Part 1

Details Fixed points and fusion rings. Part 1 Fixed points and fusion rings. Part 1

2011-11-14

arxiv.org/abs/1111.3099v2

Physics

High Energy Physics

High Energy Physics - Theory

22 pages

Scientific paper

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.

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