Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 5, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP05(2021)077
Keywords
Supersymmetric Effective Theories; Global Symmetries; Supersymmetry and Duality
Categories
Funding
- Ford Foundation Professorship of Physics at Brown University
- Brown Theoretical Physics Center
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The weight space for 4D, N-extended supersymmetrical representations is conjectured to be embedded within the permutahedra associated with permutation groups. Evidence supporting this conjecture is provided by Adinkras and Coxeter Groups associated with minimal representations of 4D, N = 1 supersymmetry. The observation suggests a new approach to solving the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of permutation groups.
A conjecture is made that the weight space for 4D, N-extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups ?(d). Adinkras and Coxeter Groups associated with minimal representations of 4D, N = 1 supersymmetry provide evidence supporting this conjecture. It is shown that the appearance of the mathematics of 4D, 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 ?(d).
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