Central Extensions of Finite Heisenberg Groups in Cascading Quiver Gauge Theories

Details Central Extensions of Finite Heisenberg Groups in Cascading Quiver Gauge Theories Central Extensions of Finite Heisenberg Groups in Cascading Quiver Gauge Theories

2006-03-14

arxiv.org/abs/hep-th/0603114v1

Nucl.Phys.B749:245-265,2006

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 12 figures

Scientific paper

10.1016/j.nuclphysb.2006.05.020

Many conformal quiver gauge theories admit nonconformal generalizations. These generalizations change the rank of some of the gauge groups in a consistent way, inducing a running in the gauge couplings. We find a group of discrete transformation that acts on a large class of these theories. These transformations form a central extension of the Heisenberg group, generalizing the Heisenberg group of the conformal case, when all gauge groups have the same rank. In the AdS/CFT correspondence the nonconformal quiver gauge theory is dual to supergravity backgrounds with both five-form and three-form flux. A direct implication is that operators counting wrapped branes satisfy a central extension of a finite Heisenberg group and therefore do not commute.

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