From WZW models to Modular Functors
Abstract
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.
Cite
@article{arxiv.1009.2245,
title = {From WZW models to Modular Functors},
author = {Eduard Looijenga},
journal= {arXiv preprint arXiv:1009.2245},
year = {2011}
}
Comments
In this revision (2) we give a somewhat clearer exposition of projectively flat connections (Sect. 1) and of the passage to a topological interpretation of the story (Sect. 7). Otherwise the modifications are minor. It will appear in the Handbook of Moduli