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 𝕊d. Adinkras and Coxeter Groups associated with minimal representations of 4D, \( \mathcal{N} \) = 1 supersymmetry provide evidence supporting this conjecture. It is shown that 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 𝕊d.
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Cianciara, A.J., James Gates, S., Hu, Y. et al. The 300 “correlators” suggests 4D, \( \mathcal{N} \) = 1 SUSY is a solution to a set of Sudoku puzzles. J. High Energ. Phys. 2021, 77 (2021). https://doi.org/10.1007/JHEP05(2021)077
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DOI: https://doi.org/10.1007/JHEP05(2021)077