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 in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.

Revised version

References in corpus (4)

• Conformal Field Theory, Tensor Categories and Operator Algebras
• Structure and Classification of Superconformal Nets
• A Remark on CFT Realization of Quantum Doubles of Subfactors. Case Index < 4
• Transgressive loop group extensions

Cited by in corpus (1)

• From vertex operator superalgebras to graded-local conformal nets and back