Weyl Superspace

TL;DR

This paper demonstrates that the equations of motion for eleven-dimensional supergravity can be derived from specific torsion tensor conditions in superspace, using a specialized connection in the relevant Lie algebra.

Contribution

It introduces a connection valued in the Lie algebra of Spin(1,10)×R^+ that simplifies deriving supergravity equations from superspace torsion conditions.

Findings

Equations of motion follow from torsion tensor conditions

Introduction of a new connection in the Lie algebra simplifies derivation

Provides a geometric proof of supergravity equations

Abstract

It is shown that the equations of motion of eleven-dimensional supergravity follow from setting the dimension zero components of the superspace torsion tensor equal to the Dirac matrices. The proof of this assertion is facilitated by the introduction of a connection taking its values in the Lie algebra of $Spin(1,10)\times R^+$.