Affine su(3) and su(4) fusion multiplicities as polytope volumes

Details Affine su(3) and su(4) fusion multiplicities as polytope volumes Affine su(3) and su(4) fusion multiplicities as polytope volumes

2001-06-29

arxiv.org/abs/hep-th/0106287v1

J.Phys.A35:6939-6952,2002

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, LaTeX

Scientific paper

10.1088/0305-4470/35/32/313

Affine su(3) and su(4) fusion multiplicities are characterised as discretised volumes of certain convex polytopes. The volumes are measured explicitly, resulting in multiple sum formulas. These are the first polytope-volume formulas for higher-rank fusion multiplicities. The associated threshold levels are also discussed. For any simple Lie algebra we derive an upper bound on the threshold levels using a refined version of the Gepner-Witten depth rule.

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