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

TL;DR

This paper develops a framework for Weyl covariance in 10D superspaces, proposing supergravity prepotentials and deriving superfield Weyl transformations, advancing the understanding of supergeometrical structures in high-dimensional supersymmetry.

Contribution

It introduces the first off-shell supergeometrical Weyl field strength tensors in 10D superspaces and identifies ten possible superfield supergravity prepotentials.

Findings

Derived infinitesimal 10D superspace Weyl transformation laws.

Proposed ten candidate superfield supergravity prepotentials.

Presented the first off-shell supergeometrical Weyl field strength tensors.

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.