Lifshitz backgrounds from 10d supergravity

TL;DR

The paper investigates whether Lifshitz spacetimes can be embedded in 10D supergravity via flux compactifications on SU(3)-structure manifolds. It shows a no-go for static Lifshitz in ordinary IIA, but demonstrates explicit cosmological Lifshitz solutions in IIA$^*$, and with running scalars finds Lifshitz configurations in IIB$^*$ and a Euclidean Lifshitz solution in Euclidean IIB with $z=-2$. The results highlight how ghostlike RR sectors (IIA$^*$, IIB$^*$) can realize Lifshitz geometries that are unavailable in standard IIA/IIB setups, and discuss regularity and interpretation issues related to running axion-dilaton fields. The work suggests exploring broader 4D effective theories, such as gauged $ obreak{N}=2$ supergravities with massive tensor multiplets, as fertile ground for further Lifshitz embeddings in string theory.

Abstract

We investigate whether 4-dimensional static and cosmological Lifshitz solutions can be found from deforming the existing (A)dS_4 compactifications in IIA and IIA* supergravity. Using a well motivated compactification Ansatz on SU(3)-structure manifolds with 19 undetermined parameters we demonstrate that this is not the case in ordinary IIA supergravity, thereby generalising previous nogo results in different ways. On the other hand, for IIA* we construct explicit cosmological Lifshitz solutions. We also consider solutions with non-constant scalars and are able to find simple static and cosmological Lifshitz solutions in IIB* supergravity and a Euclidean Lifshitz solution in ordinary Euclidean IIB supergravity, which is similar to a non-extremal deformation of the D-instanton. The latter solutions have z=-2.