Counting Operators in $N=1$ Supersymmetric Gauge Theories

Following a recent publication, in this paper we count the number of independent operators at arbitrary mass dimension in $N=1$ supersymmetric gauge theories and derive their field and derivative content. This work uses Hilbert series machinery and extends a technique from our previous work on handling integration by parts redundancies to vector superfields. The method proposed here can be applied to both abelian and non-abelian gauge theories and for any set of (chiral/antichiral) matter fields. We work through detailed steps for the abelian case with single flavor chiral superfield at mass dimension eight, and provide other examples in the appendices.