Mathematics – K-Theory and Homology
Scientific paper
2010-12-07
Mathematics
K-Theory and Homology
47 pages
Scientific paper
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.
Evans David E.
Gannon Terry
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