A twist on broken U(3) $$\times $$ U(3) supersymmetry

Abstract

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) $$\times $$ SU(3) $$\times $$ U(1) $$\times $$ U(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) $$\times $$ SU(3) $$\times $$ SU(3) $$\times $$ SU(3) Grand Unified Theory (GUT). $${\hbox {Sin}}^2$$ of the Weinberg angle for the GUT is 1/4 rather than 3/8, leading to a lower unification scale than usually contemplated, $$\sim 10^9 \, \hbox {GeV}$$ . After spontaneous gauge symmetry breaking to SU(3) $$\times $$ SU(2) $$\times $$ U(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.