  We derive the exact supergravity profile for the twisted scalar field emitted
by a system of fractional D3 branes at a Z2 orbifold singularity supporting N=2
quiver gauge theories with unitary groups and bifundamental matter. At the
perturbative level this twisted field is "dual" to the gauge coupling but it is
corrected non-perturbatively by an infinite tower of fractional D-instantons.
The explicit microscopic description allows to derive the gravity profile from
disk amplitudes computing the emission rate of the twisted scalar field in
terms of chiral correlators in the dual gauge theory. We compute these quantum
correlators using multi-instanton localization techniques and/or Seiberg-Witten
analysis. Finally, we discuss a non-perturbative relation between the twisted
scalar and the effective coupling of the gauge theory for some simple choices
of the brane set ups.
