### 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) |
---|---|

Pages (from-to) | 43-78 |

Number of pages | 36 |

Journal | Nuclear Physics B |

Volume | 315 |

Issue number | 1 |

DOIs | |

State | Published - Mar 13 1989 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*315*(1), 43-78. https://doi.org/10.1016/0550-3213(89)90448-3

**(Super)conformal algebra on the (super)torus.** / Mezincescu, Alexandru; Nepomechie, Rafael; Zachos, Cosmas K.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 315, no. 1, pp. 43-78. https://doi.org/10.1016/0550-3213(89)90448-3

}

TY - JOUR

T1 - (Super)conformal algebra on the (super)torus

AU - Mezincescu, Alexandru

AU - Nepomechie, Rafael

AU - Zachos, Cosmas K.

PY - 1989/3/13

Y1 - 1989/3/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=25544454840&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25544454840&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(89)90448-3

DO - 10.1016/0550-3213(89)90448-3

M3 - Article

AN - SCOPUS:25544454840

VL - 315

SP - 43

EP - 78

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1

ER -