Foliated backgrounds for M-Theory Compactifications (II)

Abstract

We summarize the foliation approach to N = 1 compactifications of eleven dimensional supergravity on eight-manifolds M (without boundary) down to AdS3 spaces for the case when the internal part ξ of the supersymmetry generator is chiral on some proper subset W of M. In this case, a topological no-go theorem implies that the complement M \ W must be a dense open subset, while M admits a singular foliation F (in the sense of Haefliger) which is defined by a closed one-form ω and is endowed with a longitudinal G2 structure. The geometry of this foliation is determined by the supersymmetry conditions. We also describe the topology of F in the case when ω is a Morse form. © 2016, Editura Academiei Romane. All rights reserved