No cosmological D = 11 supergravity

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.