Non-perturbative gauge/gravity correspondence in N=2 theories

TL;DR

This paper derives an exact supergravity profile for a twisted scalar field emitted by fractional D3 branes in an N=2 gauge theory setup, incorporating non-perturbative D-instanton effects and relating it to gauge couplings.

Contribution

It provides a non-perturbative gauge/gravity correspondence for N=2 theories by computing the twisted scalar field profile including instanton corrections.

Findings

Explicit supergravity profile including non-perturbative effects

Relation between twisted scalar and gauge coupling established

Use of multi-instanton localization and Seiberg-Witten techniques

Abstract

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.