On-shell equivalence of light-like integrability and canonical constraints for D = 10, N = 1 supergravity

Abstract

Using Weyl transformation in superspace, we prove that the noncanonical version of D = 10, N = 1 supergravity based on geometrical constraints obtained by Chau and Milewski, is equivalent on-shell to the canonical formulation. We interpret the appearance of auxiliary components for the off-shell D = 10, N = 1 supergravity multiplet as a feature of the geometrical formulation. The analysis of the implications of the Bianchi identities in the geometrical version of the theory is extended to the nonlinear case, completing the proof that Chau-Milewski constraints actually describe Poincaré supergravity. We show the failure of light-like integrability requirements by coupling supergravity to a Yang-Mills multiplet.