Brane Tilings and Specular Duality

TL;DR

This paper introduces a new duality in 4d N=1 supersymmetric quiver gauge theories represented by brane tilings, linking theories with identical master spaces via Hilbert series analysis.

Contribution

It identifies a novel duality that pairs theories sharing the same master space, expanding understanding of gauge theory moduli spaces through brane tilings and Hilbert series.

Findings

The duality relates theories with identical master spaces.

Hilbert series encode generators and relations of the moduli space.

Examples with reflexive toric diagrams illustrate the duality.

Abstract

We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which have the same combined mesonic and baryonic moduli space, otherwise called the master space. We obtain the associated Hilbert series which encodes both the generators and defining relations of the moduli space. We illustrate our findings with a set of brane tilings that have reflexive toric diagrams.