Infinite-Dimensional Algebraic $\mathfrak{Spin}$($N$) Structure in Extended/Higher Dimensional SUSY Holoraumy for Valise and On-Shell Supermultiplet Representations

Abstract

We explore the relationship between holoraumy and Hodge duality beyond four dimensions. We find this relationship to be ephemeral beyond six dimensions: it is not demanded by the structure of such supersymmetrical theories. In four dimensions for the case of the vector-tensor $\mathcal{N}$ = 4 multiplet, however, we show that such a linkage is present. Reduction to 1D theories presents evidence for a linkage from higher-dimensional supersymmetry to an infinite-dimensional algebra extending $\mathfrak{Spin}(N)$.

arXiv comment40 pages, includes connections to 4D, N=4 Vector Chiral multiplet and SM-i sub-multiplets, corrected some typos, updated institutional affiliations

References in corpus (18)

• When Superspace Is Not Enough
• Adinkra (In)Equivalence From Coxeter Group Representations: A Case Study
• On Clifford-Algebraic "Holoraumy", Dimensional Extension, and SUSY Holography
• Adinkras and SUSY Holography
• A Lorentz Covariant Holoraumy-Induced "Gadget" From Minimal Off-Shell 4D, N = 1 Supermultiplets
• Adinkras, 0-branes, Holoraumy and the SUSY QFT/QM Correspondence
• On the Four Dimensional Holoraumy of the 4D, $\mathcal{N}$ = 1 Complex Linear Supermultiplet
• The 300 "Correlators" Suggests 4D, $\mathcal{N}$ = 1 SUSY Is a Solution to a Set of Sudoku Puzzles
• Generating all 36,864 Four-Color Adinkras via Signed Permutations and Organizing into $\ell$- and $\tilde{\ell }$-Equivalence Classes
• Is It Possible To Embed A 4D, N = 4 Supersymmetric Vector Multiplet Within A Completely Off-Shell Adinkra Hologram?
• Think Different: Applying the Old Macintosh Mantra to the Computability of the SUSY Auxiliary Field Problem
• On Linearized Nordstr\" om Supergravity in Eleven and Ten Dimensional Superspaces (2)
• A Detailed Investigation of First and Second Order Supersymmetries for Off-Shell N = 2 and N = 4 Supermultiplets
• 4D N=1 Kaluza-Klein superspace
• Examples of 4D, N = 2 Holoraumy
• On the Ubiquity Of Electromagnetic-Duality Rotations in 4D, N = 1 Holoraumy Tensors for On-Shell 4D Supermultiplets
• 4D, $\mathcal{N}=1$ Matter Gravitino Genomics
• Exploring the Abelian 4D, $\mathcal{N}$ = 4 Vector-Tensor Supermultiplet and Its Off-Shell Central Charge Structure