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- Title
Loop groups and noncommutative geometry.
- Authors
Carpi, Sebastiano; Hillier, Robin
- 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 projective unitary positive-energy representations of any given loop group . The construction is based on certain supersymmetric conformal field theory models associated with 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.
- Subjects
TOPOLOGICAL groups; NONCOMMUTATIVE differential geometry; REPRESENTATION theory; CONFORMAL field theory; RING theory
- Publication
Reviews in Mathematical Physics, 2017, Vol 29, Issue 9, p-1
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X17500295