Abstract
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 G 2 × G 2 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.
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