Triangle Seminars

Abstract:
The existence of a modular invariant genus two partition function
implies infinitely many relations among the structure constants of a
chiral self-dual conformal field theory. All of these relations can be
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.