What symmetry breaking would be required for gauginos from a supersymmetric theory to behave like left-handed quarks of the Standard Model? Starting with a supersymmetric SU(3)xSU(3)xU(1)xU(1) gauge theory, the 18 adjoint-representation gauginos are replaced with 2 families of 9 gauginos in the (3,3*) representation of the group. After this explicit breaking of supersymmetry, two-loop quadratic divergences still cancel at a unification scale. Coupling constant unification is supported by deriving the theory from an SU(3)xSU(3)xSU(3)xSU(3) Grand Unified Theory (GUT). Sin2 of the Weinberg angle for the GUT is 1/4 rather than 3/8, leading to a lower unification scale than usually contemplated, ~109 GeV. After spontaneous gauge symmetry breaking to SU(3)xSU(2)xU(1), the theory reproduces the main features of the Standard Model for two families of quarks and leptons, with gauginos playing the role of left-handed quarks and sleptons playing the role of the Higgs boson. An extension to the theory is sketched that incorporates the third family of quarks and leptons.
Chapman, S. A twist on broken U(3) × U(3) supersymmetry. Quantum Stud.: Math. Found. (2020). https://doi.org/10.1007/s40509-020-00232-8