  We describe the structure of the vacuum states of quiver gauge theories
obtained via dimensional reduction over homogeneous spaces, in the explicit
example of SU(3)-equivariant dimensional reduction of Yang-Mills-Dirac theory
on manifolds of the form M x CP(2). We pay particular attention to the role of
topology of background gauge fields on the internal coset spaces, in this case
U(1) magnetic monopoles and SU(2) instantons on CP(2). The reduction of
Yang-Mills theory induces a quiver gauge theory involving coupled
Yang-Mills-Higgs systems on M with a Higgs potential leading to dynamical
symmetry breaking. The criterion for a ground state of the Higgs potential can
be written as the vanishing of a non-abelian Yang-Mills flux on the quiver
diagram, regarded as a lattice with group elements attached to the links. The
reduction of SU(3)-symmetric fermions yields Dirac fermions on M transforming
under the low-energy gauge group with Yukawa couplings. The fermionic zero
modes on CP(2) yield exactly massless chiral fermions on M, though there is a
unique choice of spin(c) structure on CP(2) for which some of the zero modes
can acquire masses through Yukawa interactions. We work out the spontaneous
symmetry breaking patterns and determine the complete physical particle
spectrum in a number of explicit examples, some of which possess quantum number
assignments qualitatively analogous to the manner in which vector bosons,
quarks and leptons acquire masses in the standard model.
