Central Extensions of Finite Heisenberg Groups in Cascading Quiver Gauge Theories
arXiv:hep-th/0603114 · doi:10.1016/j.nuclphysb.2006.05.020
Abstract
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.
arXiv comment25 pages, 12 figures
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- Discrete Symmetries in Dimer Diagrams
- Comments on D-branes on Orbifolds and K-theory