## Abstract

A systematic analysis of the genus two vacuum amplitudes of chiral self-dual conformal field theories is performed. It is explained that the existence of a modular invariant genus two partition function implies infinitely many relations among the structure constants of the theory. All of these relations are shown to be a consequence of the associativity of the operator product expansion, as well as the modular covariance properties of the torus one-point functions. Using these techniques we prove that for the proposed extremal conformal field theories at c = 24k a consistent genus two vacuum amplitude exists for all k, but that this does not actually check the consistency of these theories beyond what is already testable at genus one.

Original language | English (US) |
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Pages (from-to) | 295-364 |

Number of pages | 70 |

Journal | Communications in Number Theory and Physics |

Volume | 4 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2010 |

## ASJC Scopus subject areas

- Algebra and Number Theory
- Mathematical Physics
- Physics and Astronomy(all)