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) × U(1) endowed with a family of SU(3)-structures including a nearly K¨ahler structure. We derive the fixed treelevel 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 non-perturbatively 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 different points of the moduli space, some of which support consistent heterotic flux vacua.