Holographic non-perturbative corrections to gauge couplings

TL;DR

This paper derives the full F-theory background for four D7 branes by incorporating D-instanton effects, revealing the non-perturbative corrections to gauge couplings in a microscopic framework.

Contribution

It provides a microscopic derivation of the non-perturbative F-theory background for D7 branes, linking D-instanton contributions to gauge coupling corrections.

Findings

Derived the non-perturbative F-theory background explicitly.

Connected D-instanton effects to the D7 brane chiral ring.

Reconstructed the exact gauge coupling from perturbative and chiral ring data.

Abstract

We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I' theory 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 Nf=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.