4D, N=1 Supergravity Genomics

Abstract

The off-shell representation theory of 4D, $\mathcal{N}=1$ supermultiplets can be categorized in terms of distinct irreducible graphical representations called adinkras as part of a larger effort we call supersymmetry `genomics.' Recent evidence has emerged pointing to the existence of three such fundamental adinkras associated with distinct equivalence classes of a Coxeter group. A partial description of these adinkras is given in terms of two types, termed cis-and trans-adinkras (the latter being a degenerate doublet) in analogy to cis/trans isomers in chemistry. Through a new and simple procedure that uses adinkras, we find the irreducible off-shell adinkra representations of 4D, $\mathcal{N}=1$ supergravity, in the old-minimal, non-minimal, and conformal formulations. This procedure uncovers what appears to be a selection rule useful to reverse engineer adinkras to higher dimensions. We categorize the supergravity representations in terms of the number of cis-($n_c$) and trans-($n_t$) adinkras in the representation and synthesize our new results with our previous supersymmetry genomics results into a group theoretic framework.

61 pages, 19 figures, version submitted to JHEP. More motivation for the problem in the introduction, new review section on adinkras in section 2

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• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• On General Off-Shell Representations of Worldline (1D) Supersymmetry
• A Q-Continuum of Off-Shell Supermultiplets
• Generating all 36,864 Four-Color Adinkras via Signed Permutations and Organizing into $\ell$- and $\tilde{\ell }$-Equivalence Classes
• A Proposal On Culling & Filtering A Coxeter Group For 4D, N = 1 Spacetime SUSY Representations
• 4D, $\mathcal{N}=1$ Matter Gravitino Genomics
• Exploring the Abelian 4D, $\mathcal{N}$ = 4 Vector-Tensor Supermultiplet and Its Off-Shell Central Charge Structure