Supersymmetric Adler-Bardeen anomaly in N=1 super-Yang-Mills theories

TL;DR

This paper investigates the supersymmetric Adler-Bardeen anomaly in N=1 super-Yang-Mills theories across various dimensions, providing a method to solve consistency conditions and explicit solutions in ten dimensions.

Contribution

It introduces an improved descent equation method to solve the consistency conditions for supersymmetric anomalies in super-Yang-Mills theories.

Findings

Explicit solutions for the anomaly in ten-dimensional super-Yang-Mills.

A new method for solving the consistency conditions of supersymmetric anomalies.

Identification of local field polynomials for the anomalies.

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.