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

@article{Carey2004BundleGF,
  title={Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories},
  author={Alan Carey and Stuart Johnson and Michael K. Murray and Danny Stevenson and Bai-Ling Wang},
  journal={Communications in Mathematical Physics},
  year={2004},
  volume={259},
  pages={577-613}
}
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… 

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