Quark and lepton masses from deconstruction

Abstract We propose a supersymmetric SU ( 5 ) ′ × SU ( 5 ) ″ model, where the quarks and leptons live in a U ( 1 ) product group theory space that is compactified on the real projective plane RP 2 . The fermion generations are placed on different points in the deconstructed manifold by assigning them SO ( 10 ) compatible U ( 1 ) charges. The observed masses and mixing angles of quarks and leptons emerge from non-renormalizable operators involving the chiral link fields. The link fields introduce a large atmospheric neutrino mixing angle θ 23 ∼ 1 via a dynamical realization of the seesaw mechanism, which sets the deconstruction scale to a value of the order the usual B – L breaking scale ∼10 14 GeV. Supersymmetry breaking can be achieved through topological effects due to a nontrivial first homology group Z 2 . The mixed anomalies of the link fields are canceled by Wess–Zumino terms, which are local polynomials in the gauge and link fields only. We also comment on the construction of Chern–Simons couplings from these fields.