On the effective N=1 supergravity of M-theory

In the low-energy limit, M-theory compactified on S1/Z2 is formulated in terms of Bianchi identities with sources localized at orbifold singularities and anomaly-cancelling counterterms to the Wilson effective Lagrangian. Compactifying to four dimensions on a Calabi-Yau space leads to N=1 local supersymmetry. We derive a formulation of the effective supergravity which explicitly relates four-dimensional supergravity multiplets and field equations with these fundamental M-theory aspects. This formulation proves convenient for the introduction in the effective supergravity of non-perturbative M-theory contributions. It also applies to the universal sector of generic compactifications with N=1 supersymmetry