Gauge Supergravities for all Odd Dimensions

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.

Final version to appear in Int.Jour.of Theor.Phys., 12 pages, RevTeX, no figures, two columns, corrected typos in eqs.(23-29), additional reference

References in corpus (1)

• No Cosmological D=11 Supergravity

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