Affine su(2) fusion rules from gerbe 2-isomorphisms
Differential Geometry
2011-05-25 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.0909.0283,
title = {Affine su(2) fusion rules from gerbe 2-isomorphisms},
author = {Ingo Runkel and Rafal R. Suszek},
journal= {arXiv preprint arXiv:0909.0283},
year = {2011}
}
Comments
41 pages, 1 figure (the published version)