Carpi, Sebastiano and Hillier, Robin Oliver (2017) Loop groups and noncommutative geometry. Reviews in Mathematical Physics, 29 (9): 1750029. ISSN 0129-055X
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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 ℓℓ projective unitary positive-energy representations of any given loop group LGLG. The construction is based on certain supersymmetric conformal field theory models associated with LGLG 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.