Holographic Models for Theories with Hyperscaling Violation

TL;DR

This paper explores gravitational models supporting hyperscaling-violating Lifshitz space-times, analyzing their properties, stability bounds, and possible UV completions, with applications to holographic duals of condensed matter systems.

Contribution

It introduces a comprehensive gravitational framework for hvLif space-times, including stability analysis, probe field dynamics, and UV completion strategies, advancing holographic modeling of condensed matter phenomena.

Findings

Derived Breitenlohner-Freedman bounds for probe fields.

Identified conditions for hvLif space-times to have AdS or Lifshitz UV completions.

Analyzed reductions of Schrödinger and brane solutions within supergravity contexts.

Abstract

We study in detail a variety of gravitational toy models for hyperscaling-violating Lifshitz (hvLif) space-times. These space-times have been recently explored as holographic dual models for condensed matter systems. We start by considering a model of gravity coupled to a massive vector field and a dilaton with a potential. This model supports the full class of hvLif space-times and special attention is given to the particular values of the scaling exponents appearing in certain non-Fermi liquids. We study linearized perturbations in this model, and consider probe fields whose interactions mimic those of the perturbations. The resulting equations of motion for the probe fields are invariant under the Lifshitz scaling. We derive Breitenlohner-Freedman-type bounds for these new probe fields. For the cases of interest the hvLif space-times have curvature invariants that blow up in the UV. We study the problem of constructing models in which the hvLif space-time can have an AdS or Lifshitz UV completion. We also analyze reductions of Schroedinger space-times and reductions of waves on extremal (intersecting) branes, accompanied by transverse space reductions, that are solutions to supergravity-like theories, exploring the allowed parameter range of the hvLif scaling exponents.