  Gauge theories living on stacks of D7-branes are holographically related to
IIB gravitational backgrounds with a varying axion-dilaton field (F-theory).
The axion-dilaton field is generated by D7, O7 and D-instanton sources and can
be written in terms of the chiral correlators of the eight dimensional gauge
theory living on the D7-branes. Using localization techniques, we prove that
the same correlators determine the gauge coupling of the four-dimensional N=2
supersymmetric SU(2) gauge theories living on the elementary D3-brane which
probes the F-theory geometries.
