Rationality, quasirationality and finite W-algebras

Details Rationality, quasirationality and finite W-algebras Rationality, quasirationality and finite W-algebras

2000-09-28

arxiv.org/abs/hep-th/0009235v2

Commun.Math.Phys. 238 (2003) 305-331

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, AMSLaTeX; added references and clarified the relation of our results to previous work of Li et al

Scientific paper

10.1007/s00220-003-0845-1

Some of the consequences that follow from the C_2 condition of Zhu are analysed. In particular it is shown that every conformal field theory satisfying the C_2 condition has only finitely many n-point functions, and this result is used to prove a version of a conjecture of Nahm, namely that every representation of such a conformal field theory is quasirational. We also show that every such vertex operator algebra is a finite W-algebra, and we give a direct proof of the convergence of its characters as well as the finiteness of the fusion rules.

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