Remark on the Consistent Gauge Anomaly in Supersymmetric Theories

TL;DR

This paper provides a straightforward superfield calculation of the gauge anomaly in supersymmetric theories, aligning with previous results and simplifying the computational process.

Contribution

It introduces a simple, covariant superfield method for calculating gauge anomalies that matches known solutions without additional counterterms.

Findings

Superfield anomaly proportional to $d^{abc}$

Method reduces computational complexity

Results agree with Marinković's anomaly solution

Abstract

We present a direct field theoretical calculation of the consistent gauge anomaly in the superfield formalism, on the basis of a definition of the effective action through the covariant gauge current. The scheme is conceptually and technically simple and the gauge covariance in intermediate steps reduces calculational labors considerably. The resultant superfield anomaly, being proportional to the anomaly $d^{abc}=\tr T^a\{T^b,T^c\}$, is minimal without supplementing any counterterms. Our anomaly coincides with the anomaly obtained by Marinkovi\'c as the solution of the Wess-Zumino consistency condition.