Picard groups in rational conformal field theory

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dc.creatorFröhlich, Jürg
dc.creatorFuchs, Jürgen
dc.creatorRunkel, Ingo
dc.creatorSchweigert, Christoph
dc.date2004-11-23
dc.date.accessioned2026-07-07T10:50:41Z
dc.date.available2026-07-07T10:50:41Z
dc.descriptionAlgebra 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.
dc.descriptionInvited talk by C.S. at the conference on Non-commutative geometry and representation theory in mathematical physics (Karlstad, Sweden, July 2004). To appear in the proceedings
dc.identifierhttps://arxiv.org/abs/math/0411507
dc.identifierhttp://arxiv.org/abs/math/0411507
dc.identifierContemp.Math.391:85-100,2005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184614
dc.subjectCategory Theory
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.subject81T40,18D10,18D35,81T45
dc.titlePicard groups in rational conformal field theory
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