Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories
Alan L. Carey, Stuart Johnson, Michael K. Murray, Danny Stevenson, Bai-Ling Wang
Abstract
We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal G-bundle with connection and a class in H4(BG, ) for a compact semi-simple Lie group G. The Chern-Simons bundle 2-gerbe realises differential geometrically the Cheeger-Simons invariant. We apply these notions to refine the Dijkgraaf-Witten correspondence between three dimensional Chern-Simons functionals and Wess-Zumino-Witten models associated to the group G. We do this by introducing a lifting to the level of bundle gerbes of the natural map from H4(BG, ) to H3(G, ). The notion of a multiplicative bundle gerbe accounts geometrically for the subtleties in this correspondence for non-simply connected Lie groups. The implications for Wess-Zumino-Witten models are also discussed.
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