UC Berkeley

In this dissertation, we examine the holographic description of strongly-coupled quantum field theories with Lifshitz fixed points. After reviewing the standard dictionary of Lifshitz holography, we carry out the holographic renormalization procedure for two different bulk gravitational theories that support asymptotically Lifshitz spacetimes. The first bulk theory is relativistic gravity with a massive vector and the second is an anisotropic theory of gravity.

In the bulk theory of relativistic gravity with a massive vector, we find that the holographic counterterms induced near anisotropic infinity take the form of the action for Horava-Lifshitz (HL) gravity, with the appropriate value of the dynamical critical exponent z. In the particular case of 3 + 1 bulk dimensions and z = 2 asymptotic scaling near infinity, we find a logarithmic counterterm, related to anisotropic Weyl anomaly of the dual CFT, and show that this counterterm reproduces precisely the action of conformal gravity at a z = 2 Lifshitz point in 2 + 1 dimensions, which enjoys anisotropic local Weyl invariance. We find, however, that only one of two independent central charges appears in the anomaly.

We next argue that bulk HL gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without the need for additional matter. Then we show that it reproduces the full structure of the z = 2 anisotropic Weyl anomaly in dual field theories in 2 + 1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.

Finally, we search for static asymptotically Lifshitz black hole solutions in HL gravity. In contrast to general relativity, we find that these static solutions do not have black hole horizons and instead contain naked singularities. In general, we argue that it is necessary to search for stationary (but non-static) black holes with universal horizons.