Affine su(2) fusion rules from gerbe 2-isomorphisms

Details Affine su(2) fusion rules from gerbe 2-isomorphisms Affine su(2) fusion rules from gerbe 2-isomorphisms

2009-09-01

arxiv.org/abs/0909.0283v2

J.Geom.Phys. 61: 1527-1552, 2011

Mathematics

Differential Geometry

41 pages, 1 figure (the published version)

Scientific paper

10.1016/j.geomphys.2011.03.008

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.

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