Conformal nets and KK-theory
Sebastiano Carpi, Roberto Conti, Robin Hillier
TL;DR
This paper establishes a connection between conformal nets and KK-theory by identifying the fusion ring action on K-theory with a Kasparov product, bridging conformal field theory and operator algebra techniques.
Contribution
It demonstrates that the fusion ring action on K-theory can be realized as a Kasparov product, revealing a new link between conformal nets and KK-theory.
Findings
Fusion ring acts faithfully on K_0-group
Action identified with Kasparov product
Bridges conformal field theory and KK-theory
Abstract
Given a completely rational conformal net A on the circle, its fusion ring acts faithfully on the K_0-group of a certain universal C*-algebra associated to A, as shown in a previous paper. We prove here that this action can actually be identified with a Kasparov product, thus paving the way for a fruitful interplay between conformal field theory and KK-theory.
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