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

We give a geometric description of the fusion rules of the affine Lie algebra ŝu(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 ŝu(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) × 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. Email: [email protected] Email: [email protected] Address after September 2009: Department Mathematik, Bereich Algebra und Zahlentheorie, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany