On Clifford-Algebraic "Holoraumy", Dimensional Extension, and SUSY Holography

Abstract

We analyze the group of maximal automorphisms of the $N$-extended world-line supersymmetry algebra, and its action on off-shell supermultiplets. This defines a concept of "holoraumy" that extends the notions of holonomy and curvature in a novel way and provides information about the geometry of the supermultiplet field-space. In turn, the "holoraumy" transformations of 0-brane dimensionally reduced supermultiplets provide information about Lorentz transformations in the higher-dimensional spacetime from which the 0-brane supermultiplets are descended. Specifically, Spin(3) generators are encoded within 0-brane "holoraumy" tensors. World-line supermultiplets are thus able to holographically encrypt information about higher dimensional spacetime geometry.

49 pages, 11 figures, edited abstract, 2 pages added to the introduction

References in corpus (4)

• Refining the classification of the irreps of the 1D N-Extended Supersymmetry
• Spin Holography via Dimensional Enhancement
• On non-minimal N=4 supermultiplets in 1D and their associated sigma-models
• On General Off-Shell Representations of Worldline (1D) Supersymmetry

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• Adinkras From Ordered Quartets of BC${}_4$ Coxeter Group Elements and Regarding 1,358,954,496 Matrix Elements of the Gadget
• Adinkra Height Yielding Matrix Numbers: Eigenvalue Equivalence Classes for Minimal Four-Color Adinkras
• Superfield Component Decompositions and the Scan for Prepotential Supermultiplets in 10D Superspaces
• Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras
• A Proposal On Culling & Filtering A Coxeter Group For 4D, N = 1 Spacetime SUSY Representations
• Examples of 4D, N = 2 Holoraumy
• 4D, $\mathcal{N}=1$ Matter Gravitino Genomics
• On the Ubiquity Of Electromagnetic-Duality Rotations in 4D, N = 1 Holoraumy Tensors for On-Shell 4D Supermultiplets
• Infinite-Dimensional Algebraic $\mathfrak{Spin}$($N$) Structure in Extended/Higher Dimensional SUSY Holoraumy for Valise and On-Shell Supermultiplet Representations
• Exploring the Abelian 4D, $\mathcal{N}$ = 4 Vector-Tensor Supermultiplet and Its Off-Shell Central Charge Structure