  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. We scan a large class of compactifications for instanton physics and
demonstrate that many instantons have the same prefactor structure. We discuss
the associated implications and complications for moduli stabilization. We
present an explicit resolution and construction of G-flux in a generic E_6 GUT
and identify a global compactification of the local model spectral cover which
happens to facilitate prefactor computations. Via a Leray spectral sequence, we
demonstrate the relationship between right-movers of heterotic worldsheet
instantons, 3-3 strings of euclidean D3 instantons, and the Fermi zero modes of
M5-instantons.
