Lifshitz-like space-time from intersecting branes in string/M theory

TL;DR

The paper constructs 1/4 BPS, threshold F-D$p$ bound states (0≤p≤5) from the D1-D5 system via a sequence of T- and S-dualities, then analyzes their near-horizon limits. These limits yield Lifshitz-like spacetimes with dynamical exponent $z = \frac{2(5-p)}{4-p}$ and hyperscaling violation exponent $\theta = p - \frac{p-2}{4-p}$ (for $p\neq 4$), with the dilaton generally non-constant and holographic RG flows emerging in most cases. The authors provide a detailed case study for $p=0,1,2,3,5,4$, including uplifts to M-theory or S-dual frames when necessary, and show how phase structures and dual descriptions maintain Lifshitz behavior within valid parameter ranges. They also discuss a delocalized F-D1 bound state achieving an asymmetric Lifshitz form with $z=3$ and no hyperscaling violation, enriching the string-theoretic realization of nonrelativistic holography. Overall, the work offers a unified construction of Lifshitz-like holographic geometries from intersecting branes and clarifies the conditions under which they remain physically consistent.

Abstract

We construct 1/4 BPS, threshold F-D$p$ bound states (with $0\leq p \leq 5$) of type II string theories by applying S- and T-dualities to the D1-D5 system of type IIB string theory. These are different from the known 1/2 BPS, non-threshold F-D$p$ bound states. The near horizon limits of these solutions yield Lifshitz-like space-times with varying dynamical critical exponent $z=2(5-p)/(4-p)$, for $p\neq 4$, along with the hyperscaling violation exponent $θ= p - (p-2)/(4-p)$, showing how Lifshitz-like space-time can be obtained from string theory. The dilatons are in general non-constant (except for $p=1$). We discuss the holographic RG flows and the phase structures of these solutions. For $p=4$, we do not get a Lifshitz-like space-time, but the near horizon limit in this case leads to an AdS$_2$ space.