© North-Holland Publishing Company CONFORMAL SUPERGRAVITY IN TEN D IMENSIONS

We present the complete off-shell structure of conformal supergravity in ten dimensions. It is based on 128 + 128 degrees of freedom and its formulation requires differential constraints. We study how these constraints are resolved in four and five dimensions. Covariant conditions are given that restrict conformal supergravity o its on-shell Poincar6 counterpart. In ten dimensions the relationship between the two theories has new and unusual aspects, which we explore in a variety of ways. We rewrite on-shell Poincar6 supergravity in a superconformally invariant form, from which we deduce that its off-shell version must contain at least a scalar (chiral) multiplet. We analyze some aspects of the non-linear structure of the field representation based on the conformal fields combined with one scalar multiplet. 1. Introduction an