Genus two partition functions of chiral conformal field theories

Details Genus two partition functions of chiral conformal field theories Genus two partition functions of chiral conformal field theories

2010-02-17

arxiv.org/abs/1002.3371v1

Commun.Num.Theor.Phys. 4 (2010) 295-364

Physics

High Energy Physics

High Energy Physics - Theory

51 pages, 4 figures

Scientific paper

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 OPE, 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.

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