On Seven-Brane Dependent Instanton Prefactors in F-theory

Understand

We study the moduli-dependent prefactor of M5-instanton corrections to the superpotential in four-dimensional F-theory compactifications.

• In light of the M-theory and type IIb limits and also heterotic duality, we propose that the explicit moduli dependence of the prefactor can be computed by a study of zero modes localized at intersections between the instanton and seven-branes.
• We present an instanton prefactor in an E_6 F-theory GUT which does not admit a heterotic dual and show that it vanishes if and only if a point of E_8 enhancement is present in the instanton worldvolume.
• More generically, we discuss the relationship between points of E_8 and superpotential zeroes and give sufficient conditions for such a point to cause a zero, even for an SU(5) GUT.