No Cosmological D=11 Supergravity

TL;DR

This paper demonstrates that eleven-dimensional supergravity cannot be extended to include a cosmological constant, due to fundamental obstructions revealed through linearization and cohomology analyses.

Contribution

It provides the first comprehensive proof that D=11 supergravity inherently forbids a cosmological extension, contrasting with lower-dimensional supergravities.

Findings

No support for global supersymmetry in AdS background

Cohomology shows no deformations with cosmological terms

Form fields cause the obstruction to a cosmological extension

Abstract

We show, in two complementary ways, that D=11 supergravity---in contrast to all its lower dimensional versions---forbids a cosmological extension. First, we linearize the putative model about an Anti de Sitter background and show that it cannot even support a "global" supersymmetry invariance; hence there is no Noether construction that can lead to a local supersymmetry. This is true with the usual 4-form field as well as for a "dual", 7-form, starting point. Second, a cohomology argument, starting from the original full nonlinear theory, establishes the absence of deformations involving spin 3/2 mass and cosmological terms. In both approaches, it is the form field that is responsible for the obstruction. ``Dualizing'' the cosmological constant to an 11-form field also fails.