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Instantons and Toric Quiver Gauge Theories

Riccardo Argurio, Gabriele Ferretti, Christoffer Petersson

TL;DR

The paper develops a systematic, general method to construct instanton actions for gauge theories arising from D-branes at arbitrary toric singularities by higgsing from orbifold ${\cal N}=4$ theories. It derives explicit rules for how charged and neutral instanton zero modes couple to toric quiver fields, including holomorphic and anti-holomorphic sectors, and shows these rules reproduce known limits and ensure consistency under successive higgsings. The authors demonstrate the method on explicit examples—SPP, Conifold, and del Pezzo surfaces $dP_1$–$dP_3$—and use it to recover the ADS superpotential, as well as to expose stringy instanton effects and potential dynamical SUSY breaking scenarios. The work provides a practical framework for analyzing non-perturbative effects in a broad class of toric quiver gauge theories with applications to gauge dynamics and string theory phenomenology.

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.

Instantons and Toric Quiver Gauge Theories

TL;DR

The paper develops a systematic, general method to construct instanton actions for gauge theories arising from D-branes at arbitrary toric singularities by higgsing from orbifold theories. It derives explicit rules for how charged and neutral instanton zero modes couple to toric quiver fields, including holomorphic and anti-holomorphic sectors, and shows these rules reproduce known limits and ensure consistency under successive higgsings. The authors demonstrate the method on explicit examples—SPP, Conifold, and del Pezzo surfaces –—and use it to recover the ADS superpotential, as well as to expose stringy instanton effects and potential dynamical SUSY breaking scenarios. The work provides a practical framework for analyzing non-perturbative effects in a broad class of toric quiver gauge theories with applications to gauge dynamics and string theory phenomenology.

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.

Paper Structure

This paper contains 8 sections, 70 equations, 15 figures.

Table of Contents

  1. Introduction
  2. General strategy
  3. Notation and conventions
  4. Warm-up: Higgsing from $\mathbb{C}^2/\mathbb{Z}_2$ to ${\cal N}=4$
  5. Higgsing $\mathbb{C}^3/\mathbb{Z}_2\times\mathbb{Z}_2$ to the Suspended Pinch Point and further
  6. Recovering the ADS superpotential from the non-holomorphic couplings
  7. Higgsing $\mathbb{C}^3/\mathbb{Z}_3\times\mathbb{Z}_3$ to toric del Pezzo's
  8. Some applications and further directions

Figures (15)

  • Figure 1: The quiver diagram for the $\mathbb{Z}_2$ theory.
  • Figure 2: The $\mathbb{Z}_2$ theory with instantons.
  • Figure 3: The $\mathcal{N}=4$ theory higgsed down from the $\mathbb{Z}_2$ theory.
  • Figure 4: The ${\cal N}=4$ theory with instantons higgsed from the $\mathbb{Z}_2$ theory.
  • Figure 5: The SPP theory higgsed down from the $\mathbb{Z}_2\times\mathbb{Z}_2$ theory.
  • ...and 10 more figures