We explore string and $M$-theory constructions of holographic theories with Lifshitz scaling exponent $z$ and hyperscaling violation exponent $\theta$, finding a range of $z$, $\theta$ 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 ${\mathrm{AdS}}_5$ solution, in particular, gives rise to $\theta =1$ 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.

• Received 13 March 2012

DOI:https://doi.org/10.1103/PhysRevD.85.106006