Constructing Lifshitz solutions from AdS

TL;DR

The work provides a general mechanism to obtain Lifshitz spacetimes with $z=2$ from AdS vacua via circle reduction with axion flux, linking Lifshitz$_d$ to AdS$_{d+1}$ backgrounds. In four-dimensional $ ext{N}=2$ supergravity, it shows that Lifshitz$_4$ vacua inherited from $ ext{AdS}_5$ preserve 1/4 of the original supersymmetry and it constructs explicit Killing spinors, grounding the solutions in a controlled supersymmetric framework. The authors illustrate the construction through supersymmetric Type IIB truncations on squashed Sasaki–Einstein manifolds and on $T^{1,1}$, obtaining new Lifshitz embeddings and a new AdS$_4 imes S^1 imes T^{1,1}$ background. These results broaden the string-theoretic realizations of non-relativistic holography, offering explicit, BPS Lifshitz vacua and pathways to black holes and RG-flow solutions with Lifshitz asymptotics. The work thus strengthens the bridge between AdS/CFT and condensed-matter holography by embedding Lifshitz geometries in robust higher-dimensional theories.

Abstract

Under general assumptions, we show that a gravitational theory in d+1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z=2. Working in a d=4, N=2 supergravity setup, we prove that if the AdS background is N=2 supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 x S1 x T(1,1) solution of type IIB.