In earlier work we analyzed an abelianized model in which a gauged Rarita-Schwinger spin-$\frac{ 3}{ 2}$ field is directly coupled to a spin-$\frac{ 1}{ 2}$ field. Here we extend this analysis to the gauged $SU(8)$ model for which the abelianized model was a simplified substitute. We calculate the gauge anomaly, show that anomaly cancellation requires adding an additional left chiral representation $\overline{ 8}$ spin-$\frac{ 1}{ 2}$ fermion to the original fermion complement of the $SU(8)$ model, and give options for restoring boson-fermion balance. We conclude with a summary of attractive features of the reformulated $SU(8)$ model, including a possible connection to the $E_8$ root lattice.
Categories: hep-ph
