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Tambara-Yamagami, loop groups, bundles and KK-theory

Evans, David E. and Gannon, Terry 2020. Tambara-Yamagami, loop groups, bundles and KK-theory. arXiv

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This paper is part of a sequence interpreting quantities of conformal field theories K-theoretically. Here we give geometric constructions of the associated module categories (modular invariants, nimreps, etc). In particular, we give a KK-theory interpretation of all modular invariants for the loop groups of tori, as well as most known modular invariants of loop groups. In addition, we find unexpectedly that the Tambara-Yamagami fusion category has an elegant description as bundles over a groupoid, and use that to interpret its module categories as KK-elements. We establish reconstruction for the doubles of all Tambara-Yamagami categories, generalizing work of Bischoff to even-order groups. We conclude by relating the modular group representations coming from finite groups and loop groups to the Chern character and to the Fourier-Mukai transform

Item Type: Article
Date Type: Published Online
Status: Submitted
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Funders: EPSRC
Last Modified: 27 Mar 2020 08:41

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