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Type: Journal article
Title: Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories
Author: Carey, A.
Johnson, S.
Murray, M.
Stevenson, D.
Wang, B.
Citation: Communications in Mathematical Physics, 2005; 259(3):577-613
Publisher: Springer
Issue Date: 2005
ISSN: 0010-3616
Statement of
Alan L. Carey, Stuart Johnson, Michael K. Murray, Danny Stevenson and 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,Z) 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 andWess-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,Z) to H3(G,Z). The notion of a multiplicative bundle gerbe accounts geometrically for the subtleties in this correspondence for non-simply connected Lie groups. The implications forWess-Zumino-Witten models are also discussed.
Description: The original publication can be found at
DOI: 10.1007/s00220-005-1376-8
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