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Bundle Gerbes for Chern-Simons and WESS-ZUMINO-WITTEN THEORIES (2005)
| Citations: | 49 - 9 self |
BibTeX
@MISC{Carey05bundlegerbes,
author = {Alan L. Carey and Stuart Johnson and Michael K. Murray and Danny Stevenson and Bai-Ling Wang},
title = {Bundle Gerbes for Chern-Simons and WESS-ZUMINO-WITTEN THEORIES},
year = {2005}
}
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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 H 4 (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.
Keyphrases
bundle gerbes wess-zumino-witten theory wess-zumino-witten model compact semi-simple lie group cheeger-simons invariant dijkgraaf-witten correspondence chern-simons bundle 2-gerbe realises multiplicative bundle gerbe account natural map multiplicative bundle gerbes dimensional chern-simons functionals lie group
