A Class of Anomaly-Free Gauge Theories

TL;DR

This paper calculates anomaly coefficients for certain gauge theories, highlighting the special role of SU(3) and implications for the Standard Model, with coefficients vanishing under specific conditions.

Contribution

It provides a detailed calculation of anomaly coefficients for $Z_2$-graded representations of Lie algebras, emphasizing the unique role of SU(3) in anomaly cancellation.

Findings

Anomaly coefficients vanish if $G\subset SU(n)$ and $n\neq3$

The Standard Model's gauge group fits within these results

SU(3) plays a singular role in anomaly considerations

Abstract

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.