## Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II

dc.contributor.author | Mason, Geoffrey | |

dc.contributor.author | Tuite, Michael P. | |

dc.date.accessioned | 2011-12-22T13:51:40Z | |

dc.date.available | 2011-12-22T13:51:40Z | |

dc.date.issued | 2011 | |

dc.identifier.citation | Geoffrey Mason and Michael P. Tuite(2011)Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II, Geoffrey Mason and Michael P. Tuite | en_US |

dc.identifier.uri | http://hdl.handle.net/10379/2427 | |

dc.description.abstract | We continue our program to define and study $n$-point correlation functions for a vertex operator algebra $V$ on a higher genus compact Riemann surface obtained by sewing surfaces of lower genus. Here we consider Riemann surfaces of genus 2 obtained by attaching a handle to a torus. We obtain closed formulas for the genus two partition function for free bosonic theories and lattice vertex operator algebras $V_L$. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. We also compute the genus two Heisenberg vector $n$-point function and show that the Virasoro vector one point function satisfies a genus two Ward identity. We compare our results with those obtained in the companion paper, when a pair of tori are sewn together, and show that the partition functions are not compatible in the neighborhood of a two-tori degeneration point. The \emph{normalized} partition functions of a lattice theory $V_L$ \emph{are} compatible, each being identified with the genus two theta function of $L$. | |

dc.format | application/pdf | en_US |

dc.language.iso | en | en_US |

dc.subject | Mathematics - Quantum Algebra | |

dc.title | Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II | en_US |

dc.type | Article | en_US |

dc.local.publishedsource | http://arxiv.org/pdf/1111.2264 | en_US |

dc.description.peer-reviewed | peer-reviewed | en_US |

dc.local.authors | Geoffrey Mason and Michael P. Tuite | |

dc.local.arxivid | 1111.2264 | |

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