From D3-Branes to Lifshitz Space-Times

TL;DR

The paper constructs a string-theoretic realization of a $z=2$ Lifshitz spacetime within type IIB supergravity by embedding a D3-brane stack with an axion-driven plane wave, yielding a near-horizon $5$-dimensional $z=0$ Schrödinger space times $S^5$ that reduces to a $4$-dimensional $z=2$ Lifshitz spacetime upon compactification along the wave. It provides a precise Killing-spinor analysis showing a 1/4 BPS configuration, and shows that compactification breaks supersymmetry, leaving a non-supersymmetric Lifshitz background in four dimensions. The authors also present a general, analytic method to construct $z=2$ Lifshitz black branes by deforming AdS$_5$ black strings with an axion wave and reducing to 4D, illustrating the approach with explicit examples and discussing the resulting singularity structure. The work offers a concrete bridge between string theory and Lifshitz holography and outlines a scalable path to analytic Lifshitz black brane backgrounds along with considerations for holographic renormalization and boundary duals.

Abstract

We present a simple embedding of a z=2 Lifshitz space-time into type IIB supergravity. This is obtained by considering a stack of D3-branes in type IIB supergravity and deforming the world-volume by a plane wave. The plane wave is sourced by the type IIB axion. The superposition of the plane wave and the D3-branes is 1/4 BPS. The near horizon geometry of this configuration is a 5-dimensional z=0 Schroedinger space-time times a 5-sphere. This geometry is also 1/4 BPS. Upon compactification along the direction in which the wave is traveling the 5-dimensional z=0 Schroedinger space-time reduces to a 4-dimensional z=2 Lifshitz space-time. The compactification is such that the circle is small for weakly coupled type IIB string theory. This reduction breaks the supersymmetries. Further, we propose a general method to construct analytic z=2 Lifshitz black brane solutions. The method is based on deforming 5-dimensional AdS black strings by an axion wave and reducing to 4-dimensions. We illustrate this method with an example.