A cohomological gravity in D = 11

Abstract

A [Formula: see text] cohomological gravity is introduced. The central piece is a new BRST-like symmetry [Formula: see text] with [Formula: see text] up to a diffeomorphism and gauge symmetry. The only nontrivial observable of this symmetry is a Chern–Simons integral. The construction of the symmetry requires a spin 0 fermion [Formula: see text] and a spin [Formula: see text] boson [Formula: see text] at the minimum, in addition to the standard gravity and gauge fields, to close the algebra off-shell. The gravity action is uniquely determined by requiring a field redefinition type of global symmetry between bosonic and fermionic fields. It is of a simple form [Formula: see text] plus a Chern–Simons term, and appears as the [Formula: see text] supergravity action under a special combination of the fields without independent presence of [Formula: see text] and [Formula: see text]. The [Formula: see text]-invariant path-integral measure, which is also invariant under the global symmetry, is shown to exist for the theory to be valid at quantum level. It achieves only when the fields are redefined under certain combination that is different from the special combination, and the fields in this combination are interpreted as physical fields. At [Formula: see text] limit, where all field combinations converges, the theory reduces to [Formula: see text] supergravity and the global symmetry becomes the local supersymmetry with [Formula: see text] as the local variable. At a nonvanishing [Formula: see text] limit set by residue symmetries upon broken [Formula: see text]-symmetry, the theory admits a cosmological solution that has a wavy term to allow accelerated expansion of the universe while not violate null energy condition.