We present arguments to support the existence of weight spaces for supersymmetric field theories and identify the calculations of information about supermultiplets to define such spaces via the concept of “holoraumy.” For the first time, this is extended to the complex linear superfield by a calculation of the commutator of supercovariant derivatives on all of its component fields.

Adinkras are combinatorial objects developed to study supersymmetry representations. Gates et al. introduced the gadget as a function of pairs of adinkras, obtaining some mysterious results for (n = 4, k = 1) adinkras with computer-aided computation. Specifically, very few values of the gadget actually appear, suggesting a great deal of symmetry in these objects. In this paper, we compute gadgets symbolically and explain some of these observed phenomena with group theory and combinatorics. Guided by this work, we give some suggestions for generalizations of the gadget to other values of the n and k parameters.

Adinkras are combinatorial objects developed to study supersymmetry representations. Gates et al. introduced the gadget as a function of pairs of adinkras, obtaining some mysterious results for ( = 4, k = 1 ) adinkras with computer-aided computation. Specifically, very few values of the gadget actually appear, suggesting a great deal of symmetry in these objects. In this paper, we compute gadgets symbolically and explain some of these observed phenomena with group theory and combinatorics. Guided by this work, we give some suggestions for generalizations of the gadget to other values of the n and k parameters.