Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-04-12
Nucl.Phys.B757:1-18,2006
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, five figures
Scientific paper
10.1016/j.nuclphysb.2006.06.030
A large class of quiver gauge theories admits the action of finite Heisenberg groups of the form Heis(Z_q x Z_q). This Heisenberg group is generated by a manifest Z_q shift symmetry acting on the quiver along with a second Z_q 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 Z_q 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 Z_q 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 C^3/Z_3, Y^{4,2} and Y^{6,3} quiver.
Burrington Benjamin A.
Liu James T.
Mahato Manavendra
Pando Zayas Leopoldo A.
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