JOURNAL OF HIGH ENERGY PHYSICS, v.3, no., pp.116 -
We use the theory of singular foliations to study N = 1 compactifications of elevendimensional
supergravity on eight-manifolds M down to AdS3 spaces, allowing for the possibility
that the internal part ξ of the supersymmetry generator is chiral on some locus W which does
not coincide with M. We show that the complement M \W must be a dense open subset of M
and that M admits a singular foliation ¯ F endowed with a longitudinal G2 structure and defined
by a closed one form !, whose geometry is determined by the supersymmetry conditions. The
singular leaves are those leaves which meet W. When ! is a Morse form, the chiral locus is a
finite set of points, consisting of isolated zero-dimensional leaves and of conical singularities of
seven-dimensional leaves. In that case, we describe the topology of ¯ F using results from Novikov
theory. We also show how this description fits in with previous formulas which were extracted
by exploiting the Spin(7)± structures which exist on the complement of W.
Open Access, ⓒThe Authors.