Algebraic Coset Conformal Field Theories |
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Authors: | Feng Xu |
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Institution: | (1) Department of Mathematics, University of Oklahoma, 601 Elm Ave, Room 423, Norman, OK 73019, USA. E-mail: xufeng@math.ou.edu, US |
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Abstract: | All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories,
i.e., gauged Wess–Zumino–Witten (WZW) models with compact gauge groups. In this paper we use subfactor theory and ideas of
algebraic quantum field theory to approach coset Conformal Field Theories. Two conjectures are formulated and their consequences
are discussed. Some results are presented which prove the conjectures in special cases. In particular, one of the results
states that a class of representations of coset W
N
(N≥ 3) algebras with critical parameters are irreducible, and under the natural compositions (Connes' fusion), they generate
a finite dimensional fusion ring whose structure constants are completely determined, thus proving a long-standing conjecture
about the representations of these algebras.
Received: 5 November 1998 / Accepted: 18 October 1999 |
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Keywords: | |
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