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

Abstract

A conjecture is made that the weight space for 4D, $\mathcal{N}$-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, $\mathcal{N}$ = 1 supersymmetry provide evidence supporting this conjecture. It is shown the appearance of the mathematics of 4D, $\mathcal{N}$ = 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 $\mathbb{S}{}_d$.

LaTeX twice, 39 pages, 14 figures, 28 tables (v2 added one table and associated content, v3 note added in proof comment)

References in corpus (2)

• When Superspace Is Not Enough
• Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras

Cited by in corpus (4)

• There and Back Again: Mapping and Factorising Cosmological Observables
• Infinite-Dimensional Algebraic $\mathfrak{Spin}$($N$) Structure in Extended/Higher Dimensional SUSY Holoraumy for Valise and On-Shell Supermultiplet Representations
• A Letter Highlighting Matrix Mapping in Minimal 4D, $\mathcal{N}$ = 1 On-Shell Supermultiplet Representations
• A Note On Exemplary Off-Shell Constructions Of 4D, $\mathcal{N}$ = 2 Supersymmetry Representations