A Proposal On Culling & Filtering A Coxeter Group For 4D, N = 1 Spacetime SUSY Representations

Abstract

We review the mathematical tools required to cull and filter representations of the Coxeter Group $B{C}_4$ into providing bases for the construction of minimal off-shell representations of the 4D, $\mathcal{N}$ = 1 spacetime supersymmetry algebra. Of necessity this includes a description of the mathematical mechanism by which four dimensional Lorentz symmetry appears as an emergent symmetry in the context of one dimensional adinkras with four colors described by the Coxeter Group $B{C}_4$.

LaTeX twice, 1 figure, 11 ppg, (update includes comment on number of acceptable four-color adinkras)

References in corpus (5)

• On Clifford-Algebraic "Holoraumy", Dimensional Extension, and SUSY Holography
• The Real Anatomy of Complex Linear Superfields
• A Lorentz Covariant Holoraumy-Induced "Gadget" From Minimal Off-Shell 4D, N = 1 Supermultiplets
• Adinkras, 0-branes, Holoraumy and the SUSY QFT/QM Correspondence
• Adinkra `Color' Confinement In Exemplary Off-Shell Constructions Of 4D, $\mathcal{N}$ = 2 Supersymmetry Representations

Cited by in corpus (4)

• Generating all 36,864 Four-Color Adinkras via Signed Permutations and Organizing into $\ell$- and $\tilde{\ell }$-Equivalence Classes
• Adinkras From Ordered Quartets of BC${}_4$ Coxeter Group Elements and Regarding 1,358,954,496 Matrix Elements of the Gadget
• 4D, $\mathcal{N}=1$ Matter Gravitino Genomics
• Exploring the Abelian 4D, $\mathcal{N}$ = 4 Vector-Tensor Supermultiplet and Its Off-Shell Central Charge Structure