From WZW models to Modular Functors

Details From WZW models to Modular Functors From WZW models to Modular Functors

2010-09-12

arxiv.org/abs/1009.2245v2

Mathematics

Algebraic Geometry

In this revision (2) we give a somewhat clearer exposition of projectively flat connections (Sect. 1) and of the passage to a

Scientific paper

In this survey paper (which supersedes our earlier arXiv preprint math.AG/0507086) we give a relatively simple and coordinate free description of the WZW model as a local system whose base is a G_m-bundle on the moduli stack of pointed curves. We derive its main properties and show how it leads to a modular functor in the spirit of Graeme Segal (except for unitarity). The approach presented here is almost purely algebro-geometric in character; it avoids the Boson-Fermion correspondence, operator product expansions as well as Teichmueller theory.

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