Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-04-26
Nucl.Phys. B620 (2002) 537-550
Physics
High Energy Physics
High Energy Physics - Theory
14 pages, LaTeX, version to be published
Scientific paper
10.1016/S0550-3213(01)00543-0
We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain convex polytopes, and write them explicitly as multiple sums measuring those volumes. We focus on su(2), but discuss higher-point (N>3) and higher-genus fusion in a general way. The method follows that of our previous work on tensor product multiplicities, and so is based on the concepts of generalised Berenstein-Zelevinsky diagrams, and virtual couplings. As a by-product, we also determine necessary and sufficient conditions for non-vanishing higher-point fusion multiplicities. In the limit of large level, these inequalities reduce to very simple non-vanishing conditions for the corresponding tensor product multiplicities. Finally, we find the minimum level at which the higher-point fusion and tensor product multiplicities coincide.
Rasmussen Jorgen
Walton Mark A.
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