Poincare invariant gravity with local supersymmetry as a gauge theory for the M-algebra

TL;DR

This paper develops a gauge theory for the M-algebra based on a Poincare invariant gravitational action extended with local supersymmetry, differing from standard eleven-dimensional supergravity, and explores its vacuum solutions and graviton propagator.

Contribution

It introduces a new gauge theory for the M-algebra with local supersymmetry, extending the Poincare invariance, and analyzes its vacuum solutions and graviton propagation properties.

Findings

The theory describes a gauge for the M-algebra, not standard supergravity.

Vacuum solutions include warped products with de Sitter spacetime.

A nontrivial graviton propagator exists only in four dimensions with positive cosmological constant.

Abstract

Here we consider a gravitational action having local Poincare invariance which is given by the dimensional continuation of the Euler density in ten dimensions. It is shown that the local supersymmetric extension of this action requires the algebra to be the maximal extension of the N=1 super-Poincare algebra. The resulting action is shown to describe a gauge theory for the M-algebra, and is not the eleven-dimensional supergravity theory of Cremmer-Julia-Scherk. The theory admits a class of vacuum solutions of the form S^{10-d} x Y_{d+1}, where Y_{d+1} is a warped product of R with a d-dimensional spacetime. It is shown that a nontrivial propagator for the graviton exists only for d=4 and positive cosmological constant. Perturbations of the metric around this solution reproduce linearized General Relativity around four-dimensional de Sitter spacetime.