Brane instantons and fluxes in F-theory

We study the combined effect of world-volume and background fluxes on Euclidean D3-brane instantons in F-theory compactifications. We derive an appropriate form of the fermionic effective action, in which the fermions are topologically twisted and the dynamical effect of fluxes, non-trivial axio-dilaton and warping is taken into account. We study the structure of fermionic zero modes, which determines the form of possible nonperturbative superpotential and F-terms in the four-dimensional effective action. Invariance under SL(2, Z) is discussed in detail, which allows for an interpretation of the results in terms of the dual M5-brane instanton in the M-theory picture. We also provide the perturbative IIB description in the orientifold limit, when available. Furthermore, we consider the possible inclusion of supersymmetry breaking bulk fluxes and discuss its implications.