Geometry of eleven-dimensional supergravity

Abstract

A new geometrical form of the d = 11 supergravity lagrangian is suggested. This lagrangian depends on the vielbein e ω m , on the spin connection w ̂ ω mn and on the gravitino Ψ ω α. The 3-index gauge potential A ωνλ(e, w ̂ , Ψ) in this theory is a supercovariant torsion tensor. The eleven-dimensional supercovariant curvature tensor is that of non-riemannian geometry.