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Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories

2005; Springer Science+Business Media; Volume: 259; Issue: 3 Linguagem: Inglês

10.1007/s00220-005-1376-8

1432-0916

Alan L. Carey, Stuart Johnson, Michael K. Murray, Danny Stevenson, Bai‐Ling Wang,

Black Holes and Theoretical Physics

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 $H^4(BG, \ZZ)$ 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 $H^4(BG, \ZZ)$ to $H^3(G, \ZZ)$. 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.