A Note on Gauge Anomaly Cancellation in Effective Field Theories

TL;DR

This paper revisits gauge anomaly cancellation conditions in effective field theories, demonstrating that anomalies from non-renormalizable sectors can be canceled by local counterterms, simplifying anomaly conditions to fermion charge assignments.

Contribution

It provides an explicit computation of gauge anomalies in SMEFT-like models, showing non-renormalizable contributions can be canceled, aligning anomaly conditions with those of renormalizable theories.

Findings

Anomalies from non-renormalizable sectors can be canceled by local counterterms.

Gauge anomaly cancellation depends solely on fermion charge assignments.

Explicit model confirms theoretical predictions about anomaly structure in EFTs.

Abstract

The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.