Supersymmetric Adler–Bardeen anomaly in [formula omitted] super-Yang–Mills theories

Abstract

We provide a study of the supersymmetric Adler–Bardeen anomaly in the N = 1 , d = 4 , 6 , 10 super-Yang–Mills theories. We work in the component formalism that includes shadow fields, for which Slavnov–Taylor identities can be independently set for both gauge invariance and supersymmetry. We find a method with improved descent equations for getting the solutions of the consistency conditions of both Slavnov–Taylor identities and finding the local field polynomials for the standard Adler–Bardeen anomaly and its supersymmetric counterpart. We give the explicit solution for the ten-dimensional case.