Gauge Supergravities for All Odd Dimensions

Abstract

Recently proposed supergravity theories in odddimensions whose fields are connection one-forms for theminimal supersymmetric extensions of anti-de Sittergravity are discussed. Two essential ingredients are required for this construction: (1) Thesuperalgebras, which extend the adS algebra fordifferent dimensions, and (2) the Lagrangians, which areChern-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 thatthe actions are invariant by construction under thegauge supergroup and, in particular, under localsupersymmetry. Thus, unlike standard supergravity, the localsupersymmetry algebra closes off-shell and withoutrequiring auxiliary fields. The superalgebras areconstructed 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 isconstructed for D = 5, 7, and 11. In all cases the field content includes the vielbein(e ^a_μ ), the spin connection(ω ^ab_μ ), N gravitini(ψ ⁱ_μ ), and some extrabosonic "matter" fields which vary from onedimension to another.