A Note on Supersymmetric Type II Solutions of Lifshitz Type

TL;DR

This paper explores supersymmetric Type II string theory solutions exhibiting Lifshitz-like anisotropic scaling, revealing a correspondence between lower-dimensional non-relativistic vacua and higher-dimensional relativistic solutions, with implications for scale-invariant theories.

Contribution

It demonstrates how supersymmetric four-dimensional Poincaré invariant backgrounds can lead to anisotropic Lifshitz solutions, extending the understanding of non-relativistic holography in string theory.

Findings

Establishes a link between 4D Lifshitz vacua and 5D relativistic solutions.

Shows supersymmetric solutions with anisotropic scaling in Type IIB.

Provides a framework for interpolating between different scale-invariant backgrounds.

Abstract

We discuss a class of supersymmetric type II non-relativistic solutions with exact or asymptotic scale invariance. As already emerged from previous investigations, we find a clear correspondence between anisotropic d-dimensional vacua and relativistic solutions in (d + 1)-dimensions. We will show that supersymmetric four-dimensional Poincare' invariant backgrounds in type IIB can descend to analogous solutions with anisotropic scaling in t and (x, y). This result can be applied to scale invariant theories, domain walls interpolating between four-dimensional Lifshitz vacua and more general solutions with only asymptotic or approximate scaling behaviour.