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.

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

References in corpus (1)

• On the unitary nature of abelian conformal blocks

Cited by in corpus (6)

• The Witten-Reshetikhin-Turaev invariant for links in finite order mapping tori I
• Conformal blocks from vertex algebras and their connections on ${\overline{\mathcal{M}}}_{g,n}$
• Conformal blocks for Galois covers of algebraic curves
• Conformal blocks, Verlinde formula and diagram automorphisms
• The Hitchin connection in arbitrary characteristic
• On the monodromy of the Hitchin connection