Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories
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 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.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- November 2005
- DOI:
- 10.1007/s00220-005-1376-8
- arXiv:
- arXiv:math/0410013
- Bibcode:
- 2005CMaPh.259..577C
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematical Physics;
- Mathematics - Mathematical Physics
- E-Print:
- 35 pages, xy-pic diagrams, published version