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Twining characters and Picard groups in rational conformal field theory
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.ORCID iD: 0000-0003-4081-6234
2007 (English)In: Contemporary Mathematics 442 (2007), 2007Chapter in book (Refereed)
Abstract [en]

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
2007.
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-25132OAI: oai:DiVA.org:kau-25132DiVA: diva2:598907
Available from: 2013-01-22 Created: 2013-01-22 Last updated: 2014-11-21

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http://www.ams.org/bookstore-getitem/item=conm/442http://xxx.lanl.gov/abs/math.CT/0602077

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