Abstract

Recently proposed supergravity theories in odd dimensions whose fields are connection one-forms for the minimal supersymmetric extensions of anti-de Sitter gravity are discussed. Two essential ingredients are required for this construction: (1) The superalgebras, which extend the adS algebra for different dimensions, and (2) the Lagrangians, which are Chern-Simons (2n - 1)-forms. The first item completes the analysis of van Holten and Van Proeyen, which was valid for N = 1 only. The second ensures that the actions are invariant by construction under the gauge supergroup and, in particular, under local supersymmetry. Thus, unlike standard supergravity, the local supersymmetry algebra closes off-shell and without requiring auxiliary fields. The superalgebras are constructed for all dimensions and they fall into three families: osp(m\N) for D = 2, 3, 4, mod 8, osp(N\m) for D = 6, 7, 8, mod 8, and su(m - 2, 2\N) for D = 5 mod 4, with m = 2([D/2]). The Lagrangian is constructed for D = 5, 7, and 11. In all cases the field content includes the vielbein (e(mu)(a)), the spin connection (omega(mu)(ab)), N gravitini (psi(mu)(i)), and some extra bosonic "matter" fields which vary from one dimension to another.