Lifshitz flows in IIB and dual field theories

TL;DR

This paper constructs supergravity solutions describing flows from AdS to Lifshitz spacetimes, revealing that the IR behavior depends on the deformation parameter, but the Lifshitz flows are associated with unstable dual field theories.

Contribution

It demonstrates how deformations in IIB supergravity can lead to flows between AdS and Lifshitz geometries, highlighting the conditions and instabilities involved.

Findings

Flows from AdS can approach AdS3 or Lifshitz3 in IR

Lifshitz IR flows depend only on deformation value, not character

Deformations leading to Lifshitz are unstable in the dual field theory

Abstract

We construct solutions describing flows between AdS and Lifshitz spacetimes in IIB supergravity. We find that flows from AdS$_5$ can approach either AdS$_3$ or Lifshitz$_3$ in the IR depending on the values of the deformation from AdS$_5$. Surprisingly, the choice between AdS and Lifshitz IR depends only on the value of the deformation, not on its character; the breaking of the Lorentz symmetry in the flows with Lifshitz IR is spontaneous. We find that the values of the deformation which lead to flows to Lifshitz make the UV field theory dual to the AdS$_5$ geometry unstable, so that these flows do not offer an approach to defining the field theory dual to the Lifshitz spacetime.