Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion

Rasmussen, Jorgen and Walton, Mark A. (2002) Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion. Nuclear Physics B, 620 3: 537-550. doi:10.1016/S0550-3213(01)00543-0

Author Rasmussen, Jorgen
Walton, Mark A.
Title Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion
Journal name Nuclear Physics B   Check publisher's open access policy
ISSN 0550-3213
Publication date 2002-01
Sub-type Article (original research)
DOI 10.1016/S0550-3213(01)00543-0
Open Access Status DOI
Volume 620
Issue 3
Start page 537
End page 550
Total pages 14
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Language eng
Formatted abstract
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 (script 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.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 5 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 22 Mar 2012, 12:14:38 EST by Kay Mackie on behalf of Mathematics