Solitons and Yukawa Couplings in Nearly Kähler Flux Compactifications

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 Kähler 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 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 the dynamical fermion masses and compare them at differents points of the moduli space, some of which support consistent heterotic flux vacua.