## Abstract

In this paper we construct new parafermion theories, generalizing the Z_{L} parafermion theory from integer L to rational L. These non-unitary parafermion theories (which are also defined as SL(2, R)_{L}/U(1)) have some novel features: an infinite number of currents with negative conformal dimensions for most (if not all) of them. We construct the string functions of these new parafermion theories. Generalizing Felder's BRST cohomology approach we construct from the string functions the branching functions of the SU(2)_{L} × SU(2)_{K} SU(2)_{K+L} coset theories, where both K, L are rational. New N = 2 superconformal field theories and topological field theories are also constructed. Their characters are obtained in terms of the new string functions.

Original language | English |
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Pages (from-to) | 191-240 |

Number of pages | 50 |

Journal | Nuclear Physics, Section B |

Volume | 365 |

Issue number | 1 |

DOIs | |

State | Published - 4 Nov 1991 |

### Bibliographical note

Funding Information:We thank P. Argyres, K. Dienes, B. Greene, J. Grochocinski, O. Hern~ndez, A. LeClair, E. Lyman, and M. Walton for numerous discussions. This work is supported in part by the National Science Foundation.