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  Picard groups in rational conformal field theory

Fröhlich, J., Fuchs, J., Runkel, I., & Schweigert, C. (2005). Picard groups in rational conformal field theory. In J. Fuchs, J. Mickelsson, G. Rozenblioum, A. Stolin, & A. Westerberg (Eds.), Proceedings on Noncommutative Geometry and Representation Theory in Mathematical Physics (pp. 85-100).

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-4E91-4 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-4E92-2
Genre: Conference Paper

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0411507.pdf (Preprint), 261KB
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 Creators:
Fröhlich, Jürg, Author
Fuchs, Jürgen, Author
Runkel, Ingo1, Author
Schweigert, Christoph, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the existence of sets of consistent correlation functions, to demonstrate some of their properties in a model-independent manner, and to derive explicit expressions for OPE coefficients and coefficients of partition functions in terms of invariants of links in three-manifolds. We show that a Morita class of (symmetric special) Frobenius algebras A in a modular tensor category \calc encodes all data needed to describe the correlators. A Morita-invariant formulation is provided by module categories over \calc. Together with a bimodule-valued fiber functor, the system (tensor category + module category) can be described by a weak Hopf algebra. The Picard group of the category \calc can be used to construct examples of symmetric special Frobenius algebras. The Picard group of the category of A-bimodules describes the internal symmetries of the theory and allows one to identify generalized Kramers-Wannier dualities.

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Language(s): eng - English
 Dates: 2005
 Publication Status: Issued
 Pages: -
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 Rev. Type: -
 Identifiers: eDoc: 205029
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Title: Noncommutative Geometry and Representation Theory in Mathematical Physics
Place of Event: Karlstad, Sweden
Start-/End Date: 2004-07-05 - 2004-07-10

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Title: Proceedings on Noncommutative Geometry and Representation Theory in Mathematical Physics
Source Genre: Proceedings
 Creator(s):
Fuchs, J., Editor
Mickelsson, J., Editor
Rozenblioum, G., Editor
Stolin, A., Editor
Westerberg, A., Editor
Affiliations:
-
Publ. Info: -
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 85 - 100 Identifier: ISSN: 0271-4132
ISBN: 0-8218-3718-4

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Title: Contemporary Mathematics Series
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 391 Sequence Number: - Start / End Page: - Identifier: ISSN: 0271-4132
ISBN: 0-8218-3718-4