We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a Z 2 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.

We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I by taking into account the D-instanton contributions to the emission of the axio-dilaton field in the directions transverse to the D7's. The couplings of the axio-dilaton to the D-instanton moduli modify its classical source terms which are shown to be proportional to the elements of the D7 brane chiral ring. Solving the bulk field equations with the non-perturbatively corrected sources yields the full F-theory background. This solution represents the gravitational dual of the four-dimensional theory living on a probe D3 brane of type I , namely of the N = 2 Sp(1) SYM theory with N f = 4. Our results provide an explicit microscopic derivation of the non-perturbative gravitational dual of this theory. They also explain the recent observation that the exact coupling for this theory can be entirely reconstructed from its perturbative part plus the knowledge of the chiral ring on the D7 branes supporting its flavor degrees of freedom.

We show how D-instanton corrections modify the dilaton-axion profile emitted by an O7/D7 system turning it into the non-singular F-theory background which corresponds to the effective coupling on a D3 probe.

Recently we provided a microscopic derivation of the exact supergravity profile for the twisted scalar field emitted by systems of fractional D3-branes at a Z 2 orbifold singularity. In this contribution we focus on a set-up supporting an N = 2 SYM theory with SU(2) gauge group and N f = 4. We take into account the tower of D-instanton corrections to the source terms for the twisted scalar and find that the profile of the latter can be expressed in terms of the chiral ring elements of the gauge theory. We show how the twisted scalar, which at the perturbative level represents the gravity counterpart of the gauge coupling, at the non-perturbative level is related to the effective gauge coupling in an interestingly modified way.