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

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.Comment: 15 pages, CPT-TAMU-20/9