Instantons and Toric Quiver Gauge Theories

TL;DR

This paper develops a systematic method to construct instanton actions in gauge theories derived from branes at toric singularities, using higgsing from known orbifold theories, with applications to various geometries.

Contribution

It introduces a general set of rules for constructing instanton actions in toric quiver gauge theories based on superpotential structures and higgsing techniques.

Findings

Explicit instanton actions for toric singularities like the Suspended Pinch Point and Conifold.

Validation of the method through higgsing to smaller orbifolds.

Applications demonstrated in gauge theory and stringy instantons.

Abstract

We show how to construct the general action coupling (multi)instantons to gauge theories arising from branes probing arbitrary toric singularities. We give a general set of rules for how to construct such an action given the knowledge of the superpotential for the gauge theory. The main idea is to obtain the action by higgsing a theory whose instanton dynamics is known, namely an orbifold of N=4 super Yang-Mills. We find that the couplings of the fermionic zero-modes with the holomorphic fields are dictated by the structure of the superpotential describing the toric singularity. We present explicit examples such as the Suspended Pinch Point, the Conifold and the first three del Pezzo's. We perform various checks on these results by further higgsing to smaller orbifolds and present some applications, including both gauge theory and stringy instantons.