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.

Carpi, S., Hillier, R. (2017). Loop groups and noncommutative geometry. REVIEWS IN MATHEMATICAL PHYSICS, 29(9), 1-42 [10.1142/S0129055X17500295].

Loop groups and noncommutative geometry

Carpi, Sebastiano;
2017-01-01

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.
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Conformal nets
fusion ring
spectral triples
JLO cocycles
K-theory
Carpi, S., Hillier, R. (2017). Loop groups and noncommutative geometry. REVIEWS IN MATHEMATICAL PHYSICS, 29(9), 1-42 [10.1142/S0129055X17500295].
Carpi, S; Hillier, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/252757
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