Gauge Anomaly associated with the Majorana Fermion in $8k+1$ dimensions

TL;DR

This paper demonstrates that an odd number of Majorana fermions in dimensions of the form 8k+1 exhibit a gauge anomaly similar to Witten's global anomaly, which cannot be eliminated without breaking gauge invariance.

Contribution

It introduces a simple method to show gauge anomalies for Majorana fermions in 8k+1 dimensions using SO(8) instantons on S^8, extending previous understanding.

Findings

Odd number of Majorana fermions in 8k+1 dimensions have a gauge anomaly.

The anomaly is analogous to Witten's global gauge anomaly.

The anomaly cannot be removed without losing perturbative gauge invariance.

Abstract

Using an elementary method, we show that an odd number of Majorana fermions in $8k+1$ dimensions suffer from a gauge anomaly that is analogous to the Witten global gauge anomaly. This anomaly cannot be removed without sacrificing the perturbative gauge invariance. Our construction of higher-dimensional examples ($k geq1$) makes use of the SO(8) instanton on $S^8$.