The 300 "Correlators" Suggests 4D, $\cal N$ = 1 SUSY Is a Solution to a Set of Sudoku Puzzles

TL;DR

This paper proposes that the structure of 4D, al N=1 supersymmetry representations can be understood through combinatorial and geometric frameworks related to permutation groups and Sudoku-like puzzles, offering new insights into SUSY auxiliary fields.

Contribution

It introduces a novel conjecture linking SUSY representation weight spaces to permutahedra and demonstrates equivalence to a four-color problem, suggesting new computational approaches.

Findings

Mathematical connection between SUSY representations and permutahedra.

Equivalence of SUSY representation problem to a four-color Sudoku-like puzzle.

Potential for new algorithms to solve SUSY auxiliary field issues.

Abstract

A conjecture is made that the weight space for 4D, $\cal N$-extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups ${\mathbb{S}}{}_{d}$. Adinkras and Coxeter Groups associated with minimal representations of 4D, $\cal N$ = 1 supersymmetry provide evidence supporting this conjecture. It is shown the appearance of the mathematics of 4D, $\cal N$ = 1 minimal off-shell supersymmetry representations is equivalent to solving a four color problem on the truncated octahedron. This observation suggest an entirely new way to approach the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of ${\mathbb{S}}{}_{d}$.