Finite Heisenberg groups in quiver gauge theories

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 C3, the conifold and its orbifolds and some orbifolds of the cone over Yp,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.