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

作者：Runkel Ingo; Suszek Rafal R^*

来源：Journal of Geometry and Physics, 2011, 61(8): 1527-1552.

DOI：10.1016/j.geomphys.2011.03.008

• Lie groups
• Gerbes
• Affine fusion rules

We give a geometric description of the fusion rules of the affine Lie algebra, (su) over cap (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) over cap (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.

• 出版日期2011-8