Loop groups and noncommutative geometry

Abstract

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group LG. The construction is based on certain supersymmetric conformal field theory models associated with LG. We then generalize the construction, in the setting of conformal nets, to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.Comment: Minor revisio