A Class of Anomaly-Free Gauge Theories

We report on a detailed calculation of the anomaly coefficients for the odd and even parts of the $Z_2$-graded representation $\theta$ of the Lie algebra Lie$G$ on the exterior algebra of dimension $2^n$ assuming that $G\subset U(n)$. The coefficients vanish provided $G\subset SU(n)$ and $n\ne3$. The singular role of the gauge group SU(3) is emphasized. The Standard Model is covered by this result.