Algebraic Coset Conformal field theories

Details Algebraic Coset Conformal field theories Algebraic Coset Conformal field theories

1998-10-06

arxiv.org/abs/math/9810035v2

Commun.Math.Phys. 211 (2000) 1-43

Mathematics

Operator Algebras

49 pages, Improved presentations and added details, to appear in Comm.Math.Phys

Scientific paper

10.1007/s002200050800

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 $W_N$ ($N\geq 3$) 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.

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