E3-brane instantons and baryonic operators for D3-branes on toric singularities

TL;DR

This paper explores how E3-brane instantons in string theory induce BPS operators in D3-brane world-volume theories at toric Calabi-Yau singularities, linking non-perturbative effects to the AdS/CFT correspondence.

Contribution

It demonstrates a constructive correspondence between E3-brane instantons and BPS operators in the dual gauge theory, extending the understanding of non-perturbative effects in AdS/CFT.

Findings

E3-brane instantons produce BPS baryonic and mesonic operators.

The instantons underlie the AdS/CFT map between operators and wrapped D3-branes.

Constructive proof of the correspondence supports the non-perturbative operator generation.

Abstract

We consider the couplings induced on the world-volume field theory of D3-branes at local toric Calabi-Yau singularities by euclidean D3-brane (E3-brane) instantons wrapped on (non-compact) holomorphic 4-cycles. These instantons produce insertions of BPS baryonic or mesonic operators of the four-dimensional ${\cal{N}}=1$ quiver gauge theory. We argue that these systems underlie, via the near-horizon limit, the familiar AdS/CFT map between BPS operators and D3-branes wrapped on supersymmetric 3-cycles on the 5d horizon. The relation implies that there must exist E3-brane instantons with appropriate fermion mode spectrum and couplings, such that their non-perturbative effects on the D3-branes induce operators forming a generating set for all BPS operators of the quiver CFT. We provide a constructive argument for this correspondence, thus supporting the picture.