Quiver-Invariant Dualities between Brane Tilings

TL;DR

This paper explores dualities between 4d N=1 supersymmetric gauge theories represented by brane tilings, showing how tilting mutations correspond to Seiberg dualities and preserve the moduli space.

Contribution

It introduces a novel tilting mutation method on brane tilings that captures dualities between theories with identical moduli spaces but different superpotentials.

Findings

Tilting mutations correspond to Seiberg dualities in brane tilings.

The moduli space remains invariant under these mutations.

Explicit example demonstrates the mutation process and duality correspondence.

Abstract

We study pairs of 4d N=1 supersymmetric gauge theories that share the same vacuum moduli space and the same chiral field content, encoded by a common quiver, but differ in their superpotentials. These theories arise as worldvolume theories on a D3-brane probing a toric Calabi-Yau 3-fold and admit a description in terms of bipartite graphs on a 2-torus, known as brane tilings. Using an explicit example, we show that the correspondence is realized by a single `tilting' mutation along the diagonals of hexagonal faces in the brane tiling, which is equivalent to a specific sequence of Seiberg dualities performed at distinct gauge nodes in the quiver.