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Picard groups in rational conformal field theory  Jürg Fröhlich
; Jürgen Fuchs
; Ingo Runkel
; Christoph Schweigert
;  Date: 
23 Nov 2004  Subject:  Category Theory; Mathematical Physics; Quantum Algebra MSCclass: 81T40,18D10,18D35,81T45  math.CT hepth mathph math.MP math.QA  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 modelindependent manner, and to derive explicit expressions for OPE coefficients and coefficients of partition functions in terms of invariants of links in threemanifolds. 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 Moritainvariant formulation is provided by module categories over $calc$. Together with a bimodulevalued 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 KramersWannier dualities.  Source:  arXiv, math.CT/0411507  Services:  Forum  Review  PDF  Favorites 


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