Lifshitz flows in IIB and dual field theories

We construct solutions describing flows between AdS and Lifshitz spacetimes in IIB supergravity. We find that flows from AdS$_5$ can approach either AdS$_3$ or Lifshitz$_3$ in the IR depending on the values of the deformation from AdS$_5$. Surprisingly, the choice between AdS and Lifshitz IR depends only on the value of the deformation, not on its character; the breaking of the Lorentz symmetry in the flows with Lifshitz IR is spontaneous. We find that the values of the deformation which lead to flows to Lifshitz make the UV field theory dual to the AdS$_5$ geometry unstable, so that these flows do not offer an approach to defining the field theory dual to the Lifshitz spacetime.