On Lifshitz scaling and hyperscaling violation in string theory

TL;DR

This work investigates how Lifshitz scaling with hyperscaling violation, characterized by $(z,\theta)$, can arise in string/M-theory through null deformations of AdS brane spacetimes and subsequent dimensional reductions. By analyzing AdS$_5$ null normalizable deformations and their IIA reductions, the paper identifies a Lifshitz solution with $d=2$, $(z,\theta)=(3,1)$ (i.e., $\theta=d-1$), linking to potential hidden Fermi surfaces; it then extends the analysis to M2- and M5-brane near-horizon geometries, obtaining a spectrum of $(z,\theta)$ values after reducing to D2 and D4 branes. The results are reinforced by holographic stress-tensor and scalar-probe analyses, and by mapping various UV/IR phases across different brane configurations. Overall, the paper broadens the landscape of holographic duals with nonrelativistic scaling and hyperscaling violation, offering insights into possible connections with condensed matter phenomena and the structure of entanglement in these exotic spacetimes.

Abstract

We explore string/M-theory constructions of holographic theories with Lifshitz scaling exponent $z$ and hyperscaling violation exponent $θ$, finding a range of $z,θ$-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 $AdS_5$ solution in particular gives rise to $θ=1$ 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.