  We study vacuum states and symmetric fermions in equivariant dimensional
reduction of Yang-Mills-Dirac theory over the six-dimensional homogeneous space
SU(3)/U(1)x U(1) endowed with a family of SU(3)-structures including a nearly
Kahler structure. We derive the fixed tree-level scalar potentials of the
induced Yang-Mills-Higgs theory, and compute the dynamically generated gauge
and Higgs boson masses as functions of the metric moduli of the coset space. We
find an integrable subsector of the Higgs field theory which is governed by a
sine-Gordon type model whose topological soliton solutions are determined
nonperturbatively by the gauge coupling and which tunnel between families of
infinitely degenerate vacua. The reduction of the Dirac action for symmetric
fermions yields exactly massless chiral fermions, containing subsectors which
have fixed tree-level Yukawa interactions. We compute dynamical fermion mass
matrices explicitly and compare them at differents points of the moduli space,
some of which support consistent heterotic flux vacua.
