Weyl Covariance, and Proposals for Superconformal Prepotentials in 10D Superspaces

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives $ abla{}_{underline A}$, the torsion supertensors $T{}_{{underline A} , {underline B}}{}^{{underline C}}$, and curvature supertensors $R{}_{{underline A} , {underline B}}{}_{, underline c} {}^{underline d}$ in 10D superspaces. Starting from the proposal that an unconstrained supergravity prepotential for the 11D, $mathcal{N}$ = 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, $mathcal{N}$ = 1 superfield supergravity prepotentials. The first identification of all off-shell ten dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions, is presented.