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.
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Received: 18 October 2000 / Accepted: 28 January 2003 Published online: 5 May 2003
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ID="*" Present address: Department of Mathematics, King's College London, Strand, London WC2R 2LS, U.K. E-mail: mrg@mth.kcl.ac.uk
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ID="**" Present address: Harvard University, Department of Mathematics, One Oxford Street, Cambridge, MA 02138, USA. E-mail: aneitzke@alumni.princeton.edu
Communicated by R.H. Dijkgraaf
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Gaberdiel, M., Neitzke, A. Rationality, Quasirationality and Finite W-Algebras. Commun. Math. Phys. 238, 305–331 (2003). https://doi.org/10.1007/s00220-003-0845-1
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DOI: https://doi.org/10.1007/s00220-003-0845-1