Implications of the SO(12) gauge symmetry for grand unification

Arguments following from analyzing constraints on the currently available neutral-current data are reviewed that allow for the possible existence of a neutral boson "lighter" than the one encountered in the standard $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{L+R}$ electroweak theory. An attractive possibility of accommodating this idea of a light boson in grand unified theories is to extend the popular SO(10) gauge symmetry to SO(12) gauge symmetry. It is explicitly shown that the 32-dimensional irreducible spinor representation of the SO(12) grand unified theory accommodates the electron family, which leads to the usual left-handed currents with strength $G_F$, and a "twin" electron family which leads to right-handed currents also with strength $G_F$, leaving no room for the muon ($\tau$) family.