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In earlier work we analyzed an abelianized model in which a gaugedRarita-Schwinger spin-$\frac{3}{2}$ field is directly coupled to aspin-$\frac{1}{2}$ field. Here we extend this analysis to the gauged $SU(8)$model for which the abelianized model was a simplified substitute. We calculatethe gauge anomaly, show that anomaly cancellation requires adding an additionalleft chiral representation $\overline{8}$ spin-$\frac{1}{2}$ fermion to theoriginal fermion complement of the $SU(8)$ model, and give options forrestoring boson-fermion balance. We conclude with a summary of attractivefeatures of the reformulated $SU(8)$ model, including a possible connection tothe $E_8$ root lattice.

Analysis of an $SU(8)$ model with a spin-$\frac{1}{2}$ field directly coupled to a gauged Rarita-Schwinger spin-$\frac{3}{2}$ field