English

Rationality, quasirationality and finite W-algebras

High Energy Physics - Theory 2009-10-31 v2 Quantum Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.hep-th/0009235,
  title  = {Rationality, quasirationality and finite W-algebras},
  author = {Matthias R. Gaberdiel and Andrew Neitzke},
  journal= {arXiv preprint arXiv:hep-th/0009235},
  year   = {2009}
}

Comments

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