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

Abstract

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives $\nabla {}_{\underline{A}}$, 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.

LaTeX Twice, 45 pages, v2. contains additional references, v3. includes clarification between W-Z and S-S superspace, and relation to pure spinor formulations