Superfield component decompositions and the scan for prepotential supermultiplets in 10D superspaces

Abstract The first complete and explicit SO(1,9) Lorentz descriptions of all component fields contained in the $$ \mathcal{N} $$ N = 1, $$ \mathcal{N} $$ N = 2A, and $$ \mathcal{N} $$ N = 2B unconstrained scalar 10D superfields are presented. These are made possible by a discovery of the dependence of the superfield component expansion on the branching rules of irreducible representations in one ordinary Lie algebra into one of its Lie subalgebras. Adinkra graphs for ten dimensional superspaces are defined for the first time, whose nodes depict spin bundle representations of SO(1,9). A consequential deliverable of this advance is it provides the first explicit, in terms of component fields, examples of all the off-shell 10D Nordström SG theories relevant to string theory, without off-shell central charges that are reducible but with finite numbers of fields. An analogue of Breitenlohner’s approach is implemented to scan for superfields that contain graviton(s) and gravitino(s), which are the candidates for the superconformal prepotential superfields of 10D off-shell supergravity theories and Yang-Mills theories.