Finite Heisenberg groups in quiver gauge theories

Abstract We show by direct construction that a large class of quiver gauge theories admits actions of finite Heisenberg groups. We consider various quiver gauge theories that arise as AdS/CFT duals of orbifolds of C 3 , the conifold and its orbifolds and some orbifolds of the cone over Y p , q . Matching the gauge theory analysis with string theory on the corresponding spaces implies that the operators counting wrapped branes do not commute in the presence of flux.