Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach

TL;DR

This paper develops a Hilbert series method to systematically construct and count independent operators in N=1 supersymmetric theories, accounting for redundancies and providing explicit correction formulas.

Contribution

It introduces a novel Hilbert series approach for operator basis construction in supersymmetry, including explicit correction terms and mappings for removing redundancies.

Findings

Calculates the number of independent operators at arbitrary mass dimensions.

Provides explicit formulas for removing redundancies due to equations of motion.

Demonstrates the method with several illustrative examples.

Abstract

In this paper we introduce a Hilbert series approach to build the operator basis for a N = 1 supersymmetry theory with chiral superfields. We give explicitly the form of the corrections that remove redundancies due to the equations of motion and integration by parts. In addition, we derive the maps between the correction spaces. This technique allows us to calculate the number of independent operators involving chiral and antichiral superfields to arbitrarily high mass dimension. Using this method, we give several illustrative examples.