Non-integral central extensions of loop groups

@article{Wockel2009NonintegralCE,
  title={Non-integral central extensions of loop groups},
  author={Christoph Wockel},
  journal={arXiv: Mathematical Physics},
  year={2009}
}
It is well-known that the central extensions of the loop group of a compact, simple and 1-connected Lie group are parametrised by their level $k \in Z$. This article concerns the question how much can be said for arbitrary $k \in R$ and we show that for each $k$ there exists a Lie groupoid which has the level $k$ central extension as its quotient if $k \in Z$. By considering categorified principal bundles we show, moreover, that the corresponding Lie groupoid has the expected bundle structure. 
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