Lifshitz scaling and hyperscaling violation in string theory

We explore string and M-theory constructions of holographic theories with Lifshitz scaling exponent z and hyperscaling violation exponent, finding a range of z, values. Some of these arise as effective metrics from dimensional reduction of certain kinds of null deformations of AdS spacetimes appearing in the near-horizon geometries of extremal D3-, M2-, and M5-brane theories. The AdS₅ solution, in particular, gives rise to =1 in d=2 (boundary) space dimensions. Other solutions arise as the IIA D2- and D4-brane solutions with appropriate null deformations, and we discuss the phase structure of these systems.