Twining characters and Picard groups in rational conformal field theory
2007 (English)In: Contemporary Mathematics 442 (2007), 2007Chapter in book (Refereed)
Picard groups of tensor categories play an important role in rational conformal field theory. The Picard group of the representation category C of a rational vertex algebra can be used to construct examples of (symmetric special) Frobenius algebras in C. Such an algebra A encodes all data needed to ensure the existence of correlators of a local conformal field theory.
The Picard group of the category of A-bimodules has a physical interpretation, too: it describes internal symmetries of the conformal field theory, and allows one to identify generalized Kramers-Wannier dualities of the theory.
When applying these general results to concrete models based on affine Lie algebras, a detailed knowledge of certain representations of the modular group is needed. We discuss a conjecture that relates these representations to those furnished by twining characters of affine Lie algebras
Place, publisher, year, edition, pages
Research subject Physics
IdentifiersURN: urn:nbn:se:kau:diva-25132OAI: oai:DiVA.org:kau-25132DiVA: diva2:598907