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

Pages (from-to) | 295-364 |

Number of pages | 70 |

Journal | Communications in Number Theory and Physics |

Volume | 4 |

Issue number | 2 |

State | Published - Jun 1 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Number Theory and Physics*,

*4*(2), 295-364.

**Genus two partition functions of chiral conformal field theories.** / Gaberdiel, Matthias R.; Keller, Christoph A.; Volpato, Roberto.

Research output: Contribution to journal › Article

*Communications in Number Theory and Physics*, vol. 4, no. 2, pp. 295-364.

}

TY - JOUR

T1 - Genus two partition functions of chiral conformal field theories

AU - Gaberdiel, Matthias R.

AU - Keller, Christoph A.

AU - Volpato, Roberto

PY - 2010/6/1

Y1 - 2010/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80053099177&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053099177&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:80053099177

VL - 4

SP - 295

EP - 364

JO - Communications in Number Theory and Physics

JF - Communications in Number Theory and Physics

SN - 1931-4523

IS - 2

ER -