The Bianchi Classification of Maximal D=8 Gauged Supergravities

TL;DR

This paper classifies and constructs eight-dimensional gauged supergravities from eleven-dimensional supergravity using Bianchi group manifolds, revealing new solutions including a cosmological universe model.

Contribution

It provides a comprehensive classification of maximal D=8 gauged supergravities via Bianchi group manifolds and explores their solutions and higher-dimensional uplifts.

Findings

Constructed eleven different maximal D=8 gauged supergravities.

Identified a non-supersymmetric domain wall solution describing an expanding universe.

Connected solutions to cosmological models like Einstein-de Sitter universe.

Abstract

We perform the generalised dimensional reduction of D=11 supergravity over three-dimensional group manifolds as classified by Bianchi. Thus, we construct eleven different maximal D=8 gauged supergravities, two of which have an additional parameter. One class of group manifolds (class B) leads to supergravities that are defined by a set of equations of motion that cannot be integrated to an action. All 1/2 BPS domain wall solutions are given. We also find a non-supersymmetric domain wall solution where the single transverse direction is time. This solution describes an expanding universe and upon reduction gives the Einstein-de Sitter universe in D=4. The uplifting of the different solutions to M-theory and the isometries of the corresponding group manifold are discussed.