On Lifshitz scaling and hyperscaling violation in string theory

TL;DR

This paper investigates string theory models that produce holographic duals with Lifshitz scaling and hyperscaling violation, identifying specific parameter ranges and their geometric origins from brane configurations.

Contribution

It constructs new string/M-theory backgrounds with Lifshitz and hyperscaling violation, linking these to null deformations of AdS and brane solutions, expanding the landscape of holographic models.

Findings

Identified parameter ranges for Lifshitz and hyperscaling violation exponents.

Derived effective metrics from null deformations of AdS spacetimes.

Connected specific solutions to D-brane configurations and analyzed phase structure.

Abstract

We explore string/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 $AdS_5$ 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.