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Modular invariants and twisted equivariant K-theory

Evans, David Emrys and Gannon, Terry 2009. Modular invariants and twisted equivariant K-theory. Communications in Number Theory and Physics 3 (2) , pp. 209-296. 10.4310/CNTP.2009.v3.n2.a1

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The modular invariant partition functions of conformal field theory (CFT) have a rich interpretation within von Neumann algebras (subfactors), which has led to the development of structures such as the full system (fusion ring of defect lines), nimrep (cylindrical partition function), alpha-induction, etc. Modular categorical interpretations for these have followed. More recently, Freed-Hopkins-Teleman have expressed the Verlinde ring of conformal field theories associated to loop groups as twisted equivariant K-theory. For the generic families of modular invariants (i.e. those associated to Dynkin diagram symmetries), we build on Freed-Hopkins-Teleman to provide a $K$-theoretic framework for other CFT structures, namely the full system, nimrep, alpha-induction, D-brane charges and charge-groups, etc. We also study conformal embeddings and the E7 modular invariant of SU(2), as well as some families of finite groups. This new K-theoretic framework allows us to simplify and extend the less transparent, more ad hoc descriptions of these structures obtained within CFT using loop group representation theory.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: International Press
ISSN: 1931-4523
Last Modified: 04 Jun 2017 03:10

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