Finite Heisenberg groups and Seiberg dualities in quiver gauge theories Original Research Article

A large class of quiver gauge theories admits the action of finite Heisenberg groups of the form image. This Heisenberg group is generated by a manifest image shift symmetry acting on the quiver along with a second image rephasing (clock) generator acting on the links of the quiver. Under Seiberg duality, however, the action of the shift generator is no longer manifest, as the dualized node has a different structure from before. Nevertheless, we demonstrate that the image shift generator acts naturally on the space of all Seiberg dual phases of a given quiver. We then prove that the space of Seiberg dual theories inherits the action of the original finite Heisenberg group, where now the shift generator image is a map among fields belonging to different Seiberg phases. As examples, we explicitly consider the action of the Heisenberg group on Seiberg phases for image, image and image quivers.