The action of outer automorphisms on bundles of chiral blocks

Details The action of outer automorphisms on bundles of chiral blocks The action of outer automorphisms on bundles of chiral blocks

1998-05-05

arxiv.org/abs/hep-th/9805026v3

Commun.Math.Phys. 206 (1999) 691-736

Physics

High Energy Physics

High Energy Physics - Theory

46 pages, LaTeX2e. Final version (Commun.Math.Phys., in press). We have implemented the fact that the group of automorphisms i

Scientific paper

10.1007/s002200050841

On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the Knizhnik-Zamolodchikov connection and have finite order. When all primary fields are fixed points, the isomorphisms are endomorphisms; in this case, the bundle of chiral blocks is typically a reducible vector bundle. A conjecture for the trace of such endomorphisms is presented; the proposed relation generalizes the Verlinde formula. Our results have applications to conformal field theories based on non-simply connected groups and to the classification of boundary conditions in such theories.

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