Genus two partition functions of chiral conformal field theories

Matthias R. Gaberdiel, Christoph A. Keller, Roberto Volpato

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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 languageEnglish (US)
Pages (from-to)295-364
Number of pages70
JournalCommunications in Number Theory and Physics
Issue number2
StatePublished - Jun 2010

ASJC Scopus subject areas

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


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