MSSM: A Macaulay2 Package for the Vacuum Moduli Space

Abstract

The Standard Model of particle physics has been amazingly successful at explaining interactions between three of the four fundamental forces of physics: the strong force, the weak force, and electro-magnetism. But it is an incomplete theory, failing to incorporate gravity. The Minimal Supersymmetric Standard Model (MSSM) is an approach to including gravity and supersymmetry in the standard model, by adding new particle states and interactions to the standard model. For example, supersymmetry pairs fermions (such as electrons) with bosons (such as photons). A starting point in the study of the MSSM is the Vacuum Moduli Space, which is a highly complicated algebraic variety introduced by Witten: it is the image of an affine variety X ⊆ C 49 under a symplectic quotient map to C 973 . We describe the Macaulay2 software package MSSM, which facilitates computational investigation of the Vacuum Moduli Space.