From D3-Branes to Lifshitz Space-Times

TL;DR

This paper constructs a simple embedding of z=2 Lifshitz space-times into type IIB supergravity using D3-branes and axion waves, and proposes a method to generate Lifshitz black brane solutions.

Contribution

It introduces a novel embedding of Lifshitz geometries into supergravity and a general approach to construct Lifshitz black branes via deformations of AdS black strings.

Findings

Embedded z=2 Lifshitz space-time in type IIB supergravity.

Derived a method to construct Lifshitz black branes.

Demonstrated reduction from 5D Schroedinger to 4D Lifshitz space-time.

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.