Chern-Simons Supergravities with Off-Shell Local Superalgebras

TL;DR

This paper introduces a new class of supergravity theories in odd dimensions using Chern-Simons forms, ensuring off-shell local supersymmetry without auxiliary fields, and explores their algebraic structures and potential links to M-Theory.

Contribution

It constructs explicit Chern-Simons supergravity Lagrangians in D=5, 7, 11 with off-shell supersymmetry, extending previous analyses to higher dimensions and new superalgebra families.

Findings

Supergravity theories with off-shell supersymmetry are formulated in D=5, 7, 11.

The superalgebras are classified into three families based on dimension.

Theories include dynamical fields like vielbein, spin connection, and gravitini.

Abstract

A new family of supergravity theories in odd dimensions is presented. The Lagrangian densities are Chern-Simons forms for the connection of a supersymmetric extension of the anti-de Sitter algebra. The superalgebras are the supersymmetric extensions of the AdS algebra for each dimension, thus completing the analysis of van Holten and Van Proeyen, which was valid for N=1 and for D=2,3,4,mod 8. The Chern-Simons form of the Lagrangian ensures invariance under the gauge supergroup by construction and, in particular, under local supersymmetry. Thus, unlike standard supergravity, the local supersymmetry algebra closes off-shell and without requiring auxiliary fields. The Lagrangian is explicitly given for D=5, 7 and 11. In all cases the dynamical field content includes the vielbein, the spin connection, N gravitini, and some extra bosonic ``matter'' fields which vary from one dimension to another. The superalgebras 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 possible connection between the D=11 case and M-Theory is also discussed.