Finite Heisenberg Groups in Quiver Gauge Theories

TL;DR

This paper demonstrates that many quiver gauge theories have finite Heisenberg group symmetries, linking gauge theory operators with string theory flux effects and non-commuting wrapped branes.

Contribution

It provides a direct construction showing the presence of finite Heisenberg groups in a broad class of quiver gauge theories, connecting gauge and string theory insights.

Findings

Finite Heisenberg group actions are present in various quiver gauge theories.

Operators counting wrapped branes do not commute when flux is present.

The analysis links gauge theory symmetries with string theory flux effects.

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.