Renormalisation Group Flows in Lifshitz Holography

Abstract

In this thesis we construct holographic duals of renormalisation group flows between field theories with conformal symmetries and the Lifshitz scaling symmetries. These take the form of spacetimes with a region asymptoting to AdS and another asymptoting to the Lifshitz metric of [1], with some domain wall smoothly interpolating between these regions. We first review the AdS/CFT correspondence in the context of Lorentz invariant boundary field theories, and then show how the holographic dictionary is modified by replacing the boundary field theory with one having the Lifshitz scaling symmetry. We then consider a pair of actions capable of supporting both Lifshitz and AdS spacetimes. The first of these is a massive vector field coupled to gravity and the second is the 6 dimensional Romans N = 4 massive gauged supergravity which supports 4D Lifshitz solutions. In each case we review the exact solutions that have been found previously, and then solve the linearised equations of motion around these solutions. These enable us to conjecture the existence of a variety of holographic RG flows. We then use numerical integration to confirm the existence of examples of each of these flows. In both theories we find Lifshitz to Lifshitz, AdS to Lifshitz, and Lifshitz to AdS flows. In the supergravity we also find AdS to AdS flows, and a Lifshitz to AdS flow which has an intermediate AdS region with a different dilaton value. In addition the supergravity has flows from a non-compact 6D AdS space to each of the 4D compactifications