From WZW models to modular functors

Abstract

In this survey paper we give a relatively simple and coordinate free description of the WZW model as a local system whose base is the Gm-bundle associated to the determinant 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 Segal. The approach presented here is almost purely algebro-geometric in character; it avoids the Boson-Fermion correspondence, operator product expansions as well as Teichm¨uller theory.