Higher spin BRS cohomology of supersymmetric chiral matter inD=4

Abstract

We examine the BRS cohomology of chiral matter inN=1,D=4 supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators Ψ(a, b) are products of the elementary chiral superfieldsS and\(\bar S\) and the derivative operatorsD α,\(D_\alpha ,\bar D_{\dot \beta } \) and\(\partial _{x\dot \beta } \). Such superfields Ψ(a, b) can be chosen to have “a” symmetrized undotted indices α i and “b” symmetrized dotted indices\(\dot \beta _j \). The result derived here is that each composite superfield Ψ(a,b) is subject to potential supersymmetry anomalies ifa−b is an odd number, which means that Ψ(a,b) is a fermionic superfield.