Lifshitz spacetimes from AdS null and cosmological solutions

TL;DR

<3-5 sentence high-level summary>This paper constructs explicit Lifshitz spacetimes with dynamical exponent z=2 by starting from AdS spacetimes deformed by null or cosmological scalars in ten and eleven dimensions and then performing a Kaluza-Klein reduction along a compact lightlike direction. It shows how the Lifshitz geometry emerges in lower dimensions as an effective description sourced by a massive vector field, and analyzes bulk scalar probes and the resulting holographic two-point functions, including the role of conformal dressing along the lightlike direction. The authors also discuss time-dependent AdS solutions that yield anisotropic Lifshitz scaling and present Lifshitz-like solutions in 11D via reductions and uplifts, proposing dual field theories as lightlike/deformed DLCQ variants of ${ m N}=4$ SYM and related M2-brane Chern-Simons theories. The work highlights possible RG flows between Schrödinger and Lifshitz phases and outlines several avenues for further elucidating the corresponding nonrelativistic holographic duals and their dynamics.

Abstract

We describe solutions of 10-dimensional supergravity comprising null deformations of $AdS_5\times S^5$ with a scalar field, which have $z=2$ Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by dimensional reduction of these solutions. The dual field theory in this case is a deformation of the N=4 super Yang-Mills theory. We discuss the holographic 2-point function of operators dual to bulk scalars. We further describe time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling symmetries. We also discuss deformations of $AdS\times X$ in 11-dimensional supergravity, which are somewhat similar to the solutions above. In some cases here, we expect the field theory duals to be deformations of the Chern-Simons theories on M2-branes stacked at singularities.