TY - JOUR

T1 - Loop groups and noncommutative geometry

AU - Carpi, Sebastiano

AU - Hillier, Robin Oliver

N1 - Electronic version of this article published as Loop groups and noncommutative geometry Sebastiano Carpi and Robin Hillier Reviews in Mathematical Physics 2017 29:09 in Reviews in Mathematical Physics, 29, 9, 2017, 42 Pages] 10.1142/S0129055X17500295 ©2017 World Scientific Publishing Company http://www.worldscientific.com/worldscinet/rmp

PY - 2017/10

Y1 - 2017/10

N2 - 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.

AB - 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.

KW - Conformal nets

KW - fusion ring

KW - spectral triples

KW - JLO cocycles

KW - K-theory

U2 - 10.1142/S0129055X17500295

DO - 10.1142/S0129055X17500295

M3 - Journal article

VL - 29

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 9

M1 - 1750029

ER -