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Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories | | Alan L. Carey
; Stuart Johnson
; Michael K. Murray
; Danny Stevenson
; Bai-Ling Wang
; | | Date: |
1 Oct 2004 | | Journal: | Commun.Math.Phys. 259 (2005) 577-613 | | Subject: | Differential Geometry; Mathematical Physics | math.DG math-ph math.MP | | 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 $H^4(BG, Z)$ 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 $H^4(BG, Z)$ to $H^3(G, Z)$. 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. | | Source: | arXiv, math.DG/0410013 | | Services: | Forum | Review | PDF | Favorites | |
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