Higher Spin BRS Cohomology of Supersymmetric Chiral Matter in D=4

TL;DR

This paper analyzes the BRS cohomology of chiral matter in four-dimensional N=1 supersymmetry to identify superfield operators susceptible to supersymmetry anomalies, revealing a parity-dependent anomaly condition.

Contribution

It provides a general characterization of composite superfield operators that can exhibit supersymmetry anomalies based on their index symmetry properties.

Findings

Composite superfields with odd difference in indices can have supersymmetry anomalies.

Superfield operators are classified by their index symmetry and fermionic or bosonic nature.

Potential anomalies occur specifically in fermionic superfield cases.

Abstract

We examine the BRS cohomology of chiral matter in $N=1$, $D=4$ supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators $\Y_{(a,b)}$ are products of the elementary chiral superfields $S$ and $\ov S$ and the derivative operators $D_\a$, $\ov D_{\dot \b}$ and $\pa_{\a \dot \b}$. Such superfields $\Y_{(a,b)}$ can be chosen to have `$a$' symmetrized undotted indices $\a_i$ and `$b$' symmetrized dotted indices $\dot \b_j$. The result derived here is that each composite superfield $\Y_{(a,b)}$ is subject to potential supersymmetry anomalies if $a-b$ is an odd number, which means that $\Y_{(a,b)}$ is a fermionic superfield.