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

Understand

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.