Domain wall flow equations and SU(3)×SU(3) structure compactifications

We study supersymmetric domain wall solutions in four dimensions arising from the compactification of type II supergravity on an SU(3)×SU(3) structure manifold. Using a pure spinor approach, we show that the supersymmetry variations can be reinterpreted as a generalisation of the Hitchin flow equations and describe the embedding of an SU(3)×SU(3) structure manifold into a G2×G2 structure manifold. We find a precise agreement between the four- and ten-dimensional supergravity results. The flow equations derived here should have applications in constructing the gravity duals of Chern-Simons-matter conformal field theories.