From D3-branes to Lifshitz spacetimes

Abstract

We present a simple embedding of a z = 2 Lifshitz spacetime 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 five-dimensional z = 0 Schrödinger spacetime times a 5-sphere. This geometry is also 1/4 BPS. Upon compactification along the direction in which the wave is traveling the five-dimensional z = 0 Schrödinger spacetime reduces to a four-dimensional z = 2 Lifshitz spacetime. 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 AdS5 black strings by an axion wave and reducing to four dimensions. We illustrate this method with an example.