Adinkra foundation of component decomposition and the scan for superconformal multiplets in 11D, $$ \mathcal{N} $$ = 1 superspace

Abstract For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented. Comparisons of the conceptual bases for this advance in terms of component field, superfield, and adinkra arguments, respectively, are made. These highlight the computational efficiency of the adinkra-based approach over the others. It is noted at level sixteen in the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield, the {65} representation of SO(1,10), the conformal graviton, is present. Thus, adinkra-based arguments suggest the surprising possibility that the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield alone might describe a Poincaré supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, $$ \mathcal{N} $$ N = 1 superfield supergravity. We find the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield contains 1,494 bosonic fields, 1,186 fermionic fields, and a maximum number of 29,334 links connecting them via orbits of the supercharges.