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Affine su(2) fusion rules from gerbe 2-isomorphisms | Ingo Runkel
; Rafal R. Suszek
; | Date: |
2 Sep 2009 | Abstract: | We give a geometric description of the fusion rules of the affine Lie algebra
su(2)_k at a positive integer level k in terms of the k-th power of the basic
gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy
classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The
fusion-rule coefficients are related to the existence of a 2-isomorphism
between pullbacks of these 1-isomorphisms to a submanifold of SU(2) x SU(2)
determined by the corresponding three conjugacy classes. This construction is
motivated by its application in the description of junctions of maximally
symmetric defect lines in the Wess-Zumino-Witten model. | Source: | arXiv, 0909.0283 | Services: | Forum | Review | PDF | Favorites |
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