## Abstract

A generalization of the Virasoro algebra has recently been introduced by Krichever and Novikov (KN). The KN algebra describes the algebra of general conformal transformations in a basis appropriate to a genus-g Riemann surface. We examine in detail the genus-one KN algebra, and find explicit expressions for the central extension. We, further, construct explicitly the superconformal algebra of the supertorus, which yields supersymmetric generalizations of the genus-one KN algebra. A novel feature of the odd-spin-structure case is that the algebra includes a central element which is anticommuting. We comment on possible applications to string theory.

Original language | English (US) |
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Pages (from-to) | 43-78 |

Number of pages | 36 |

Journal | Nuclear Physics, Section B |

Volume | 315 |

Issue number | 1 |

DOIs | |

State | Published - Mar 13 1989 |

## ASJC Scopus subject areas

- Nuclear and High Energy Physics