Lifshitz backgrounds from 10d supergravity

We investigate whether 4-dimensional static and cosmological Lifshitz solutions can be found from deforming the existing (A)dS_4 compactifications in IIA and IIA* supergravity. Using a well motivated compactification Ansatz on SU(3)-structure manifolds with 19 undetermined parameters we demonstrate that this is not the case in ordinary IIA supergravity, thereby generalising previous nogo results in different ways. On the other hand, for IIA* we construct explicit cosmological Lifshitz solutions. We also consider solutions with non-constant scalars and are able to find simple static and cosmological Lifshitz solutions in IIB* supergravity and a Euclidean Lifshitz solution in ordinary Euclidean IIB supergravity, which is similar to a non-extremal deformation of the D-instanton. The latter solutions have z=-2.