  The F-theory background of four D7 branes in a type I' orientifold was
conjectured to be described by the Seiberg-Witten curve for the superconformal
SU(2) gauge theory with four flavors. This relation was explained by
considering in this background a probe D3 brane, which supports this theory
with SU(2) realized as Sp(1). Here we explicitly compute the non-perturbative
corrections to the D7/D3 system in type I' due to D-instantons. This
computation provides both the quartic effective action on the D7 branes and the
quadratic effective action on the D3 brane; the latter agrees with the
F-theoretic prediction. The action obtained in this way is related to the one
derived from the usual instanton calculus \`a la Nekrasov (or from its AGT
realization in terms of Liouville conformal blocks) by means of a
non-perturbative redefinition of the coupling constant. We also point out an
intriguing relation between the four-dimensional theory on the probe D3 brane,
which has a SO(8) flavor symmetry, and the eight-dimensional dynamics on the D7
branes. On the latter, SO(8) represents a gauge group and the flavor masses
correspond to the vacuum expectation values of an adjoint scalar field m: what
we find is that the exact effective coupling in four dimensions is obtained
from its perturbative part by taking into account in its mass dependence the
full quantum dynamics of the field m in eight dimensions.
