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Published June 2010 | Published
Journal Article Open

Genus two partition functions of chiral conformal field theories

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. U sing 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.

Additional Information

© 2010 International Press. Received March 4, 2010. We thank Terry Gannon for a useful conversation and subsequent correspondence. C.A.K. thanks the Pauli Center for support during his visit to ETH. The research of M.R.G. is partially supported by the Swiss National Science Foundation, while the research of R.V. is supported by an INFN Fellowship.

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Created:
August 19, 2023
Modified:
October 20, 2023