Does SUSY know about the Standard Model?

TL;DR

This paper explores the constraints on superpotentials in supersymmetric theories derived from BRST cohomology, proposing a matrix-based superpotential that aligns with a simplified SUSY Standard Model for one lepton family.

Contribution

It introduces a novel superpotential form based on a 3x3 matrix of chiral superfields, linking BRST cohomology to Standard Model structures.

Findings

Superpotential constrained to a determinant form of a 3x3 matrix.

The proposed model aligns with a basic SUSY Standard Model for one lepton family.

The algebra supports the emergence of other lepton families through Extraordinary Invariants.

Abstract

The BRST cohomology of free chiral SUSY has a wealth of Extraordinary Invariants. When one adds a superpotential to the free theory, the extention of the Extraordinary Invariants leads to some constraints on that superpotential. A particularly simple solution of those constraints is based on a $3 \times 3$ matrix of nine chiral superfields, and then the superpotential is simply the determinant of that matrix. It is remarkable that this same theory is also a plausible basic version of the SUSY Standard Model for one Lepton family, and then the nine superfields are seen to be a left (Weak) SU(2) Lepton Doublet, Two Higgs Doublets, a Right Electron Singlet, a Right Neutrino Singlet and a Higgs singlet. Moreover, the algebra is consistent with the notion that the other two observed Lepton families arise from the coupling of the Extraordinary Invariants.