## Abstract

Let V ^{L} and V ^{R} be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let F be a conformal full field algebra over V ^{L} o× V ^{R}. We prove that the qτ -qτ̄ -traces (natural traces involving qτ = e^{2πiτ} and qτ̄ = e^{2πiτ})̄ of geometrically modified genus-zero correlation functions for F are convergent in suitable regions and can be extended to doubly periodic functions with periods 1 and τ. We obtain necessary and sufficient conditions for these functions to be modular invariant. In the case that V ^{L} = V ^{R} and F is one of those constructed by the authors in an earlier paper, we prove that all these functions are modular invariant.

Original language | English (US) |
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Pages (from-to) | 3027-3067 |

Number of pages | 41 |

Journal | Transactions of the American Mathematical Society |

Volume | 362 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2010 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics