Higher spin BRS cohomology of supersymmetric chiral matter inD=4

AbstractWe 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 operatorsDα, $$D_\alpha ,\bar D_{\dot \beta } $$ and $$\partial _{x\dot \beta } $$ . Such superfields Ψ(a, b) can be chosen to have “a” symmetrized undotted indices αi 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.