Weyl covariance, and proposals for superconformal prepotentials in 10D superspaces

Abstract

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives ∇A, the torsion supertensors TABC, and curvature supertensors RABcd in 10D superspaces. Starting from the proposal that an unconstrained supergravity prepotential for the 11D, $$ \mathcal{N} $$ N = 1 theory is described by a scalar superfield, considerations for supergravity prepotentials in the 10D theories are enumerated. We derive infinitesimal 10D superspace Weyl transformation laws and discover ten possible 10D, $$ \mathcal{N} $$ N = 1 superfield supergravity prepotentials. The first identification of all off-shell ten dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions, is presented.

Component decompositions and adynkra libraries for supermultiplets in lower dimensional superspaces

“…One can now start with any spectrum of on-shell component fields in these various dimensions and algorithmically derive the minimal dimension superfield representation (as well as alternatives) that contains this specified component field spectrum. The technique for this has been christened as an"adynkra digital analysis" (ADA) scan as described in the work of [13].…”