We construct the vacuum connection associated with a Yang-Mills theory of the graded Lie group of real, general linear transformations on superspace that is induced by supersymmetry transformations. This gives rise to a class of supersymmetric "vacuum metrics," most of which are noninvertible and/or involve theories with torsion. All of these connections are nonsingular and no limiting procedures are involved, even in the case of the original Wess-Zumino-Salam-Strathdee supersymmetric line element. Many of them are a priori compatible with the internal-symmetry group SU(2) X U(1) and extensions to include color.

• Received 14 February 1977

DOI:https://doi.org/10.1103/PhysRevD.16.304