Lifshitz scaling and hyperscaling violation in string theory

Abstract

We explore string and $M$-theory constructions of holographic theories with Lifshitz scaling exponent $z$ and hyperscaling violation exponent $\ensuremath{\theta}$, finding a range of $z$, $\ensuremath{\theta}$ 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 $\ensuremath{\theta}=1$ 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.