Tilting Mutations and Quiver-Invariant Dualities in Brane Tilings

Abstract

Quiver-invariant dualities relate distinct 4d N=1 supersymmetric gauge theories that arise as worldvolume theories on a D3-brane probing the same toric Calabi-Yau 3-fold. These dual theories share an identical quiver and differ only in their superpotentials. We show that quiver-invariant dualities are realized by tilting mutations on the brane tilings that realize these theories. Among the 42 toric phases of the H1121 model, we identify three general families of tilting mutations, all characterized by the reversal of the orientations of zig-zag paths within the mutation region of the brane tiling. We present new examples of quiver-invariant dualities, given by five doublets and one triplet of toric phases with identical quivers, for which we verify that the brane tilings related by the tilting mutations correspond to the same toric Calabi-Yau 3-fold H1121.