Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories

Carey, A.L., Johnson, S., Murray, M.K., Stevenson, D. and Wang, B.L. (2005) Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories. Communications in Mathematical Physics, 259(3), pp. 577-613. (doi:10.1007/s00220-005-1376-8)

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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 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, 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 for Wess-Zumino-Witten models are also discussed.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Stevenson, Dr Daniel
Authors: Carey, A.L., Johnson, S., Murray, M.K., Stevenson, D., and Wang, B.L.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
ISSN (Online):1432-0916
Published Online:16 June 2005

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