Isaac Chappell, S. James Gates, Jr., William D. Linch III, James Parker, Stephen Randall, Alexander Ridgway, Kory Stiffler
The off-shell representation theory of 4D, $\mathcal{N}=1$ supermultiplets can be categorized in terms of distinct irreducible graphical representations called adinkras. 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 enantiomers 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. We categorize these representations in terms of their supersymmetry `enantiomer' numbers: the number of cis-($n_c$) and trans-($n_t$) adinkras in the representation.
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http://arxiv.org/abs/1212.3318
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