The Weyl map and bundle gerbes
Differential Geometry
2019-12-13 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We introduce the notion of a general cup product bundle gerbe and use it to define the Weyl bundle gerbe on T x SU(n)/T. The Weyl map from T x SU(n)/T to SU(n) is then used to show that the pullback of the basic bundle gerbe on SU(n) defined by the second two authors is stably isomorphic to the Weyl bundle gerbe as SU(n)-equivariant bundle gerbes. Both bundle gerbes come equipped with connections and curvings and by considering the holonomy of these we show that these bundle gerbes are not D-stably isomorphic.
Cite
@article{arxiv.1910.07173,
title = {The Weyl map and bundle gerbes},
author = {Kimberly E. Becker and Michael K. Murray and Daniel Stevenson},
journal= {arXiv preprint arXiv:1910.07173},
year = {2019}
}
Comments
This paper is based on the MPhil thesis of the first author: arXiv:1910.01776. To appear in Journal of Geometry and Physics