Magnetized E3-brane instantons in F-theory

We discuss E3-brane instantons in N = 1 F-theory compactifications to four dimensions and clarify the structure of E3-E3 zero modes for general world-volume fluxes. We consistently incorporate SL(2, Z) monodromies and highlight the relation between F-theory and perturbative IIB results. We explicitly show that world-volume fluxes can lift certain fermionic zero-modes, whose presence would prevent the generation of non-perturbative superpotential terms, and we discuss in detail the geometric interpretation of the zero-mode lifting mechanism. We provide a IIB derivation of the index for generation of superpotential terms and of its modification to include world-volume fluxes, which reproduces and generalizes available results. We apply our general analysis to the explicit, though very simple, example of compactification on P-3 and its orientifold weak-coupling limit. In particular, we provide an example in which a non-rigid divisor with fluxes contributes to the superpotential.