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