Covariant Quiver Gauge Theories

Abstract

We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver bundles, and show that the reduced quiver gauge theories are all generically built on the same universal symmetry breaking pattern. The formalism enables the dimensional reduction of Chern-Simons gauge theories in arbitrary odd dimensionalities. The reduced model is a novel Chern-Simons-Higgs theory consisting of a Chern-Simons term valued in the residual gauge group plus a higher order gauge and diffeomorphism invariant coupling of Higgs fields with the gauge fields. We study the moduli spaces of solutions, which in some instances provide geometric representations of certain quiver varieties as moduli spaces of flat invariant connections. As physical applications, we consider dimensional reductions involving non-compact gauge supergroups as a means for systematically inducing novel couplings between gravity and matter. In particular, we reduce Chern-Simons supergravity to a quiver gauge theory of AdS gravity involving a non-minimal coupling to scalar Higgs fermion fields.

32 pages; v2: minor corrections, reference added

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