Dimers, Orientifolds and Anomalies

TL;DR

This paper develops geometric criteria using dimer models to determine when 4d $ abla=1$ gauge theories from D-branes at orientifolded toric singularities are anomaly-free without extra flavor branes, extending the geometric-physical correspondence.

Contribution

It introduces a method to identify anomaly-free D-brane configurations solely from toric data and orientifold types, without additional flavor branes.

Findings

Derived geometric criteria for anomaly cancellation.

Extended the geometric-physical dictionary for toric singularities.

Provided a systematic way to analyze orientifolded singularities.

Abstract

We study $4d$ $\mathcal{N}=1$ gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.