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

TL;DR

This paper extends previous abelianized models to an $SU(8)$ gauge theory with a spin-$rac{1}{2}$ field coupled to a spin-$rac{3}{2}$ field, analyzing anomaly cancellation and potential connections to $E_8$ lattice.

Contribution

It generalizes the analysis to an $SU(8)$ model, calculates gauge anomalies, and proposes fermion content modifications for anomaly cancellation and boson-fermion balance.

Findings

Anomaly cancellation requires adding an $ar{8}$ fermion representation.

Restoring boson-fermion balance involves specific fermion content adjustments.

The $SU(8)$ model shows potential links to the $E_8$ root lattice.

Abstract

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.