The Hilbert basis method for D-flat directions and the superpotential

TL;DR

This paper introduces an efficient Hilbert basis method to systematically construct D-flat directions and superpotential terms in supersymmetric gauge theories, including discrete symmetries, aiding model building.

Contribution

It extends the Hilbert basis approach to include discrete symmetries, enabling comprehensive construction of D-flat directions and superpotential terms.

Findings

Provides a complete basis for D-flat directions in supersymmetric theories

Includes discrete R and non-R symmetries in the analysis

Facilitates systematic superpotential construction

Abstract

We discuss, using the Hilbert basis method, how to efficiently construct a complete basis for D-flat directions in supersymmetric Abelian and non-Abelian gauge theories. We extend the method to discrete (R and non-R) symmetries. This facilitates the construction of a basis of all superpotential terms in a theory with given symmetries.