Holographic Models for Theories with Hyperscaling Violation

TL;DR

The work develops and analyzes several gravitational toy models that realize hvLif holography, focusing on explicit hvLif solutions with exponents such as θ=1 and z=3/2. It foregrounds the Einstein-Proca-dilaton (EPD) framework as a natural route to the full hvLif class, establishes BF-like bounds for probe fields, and investigates UV completions via AdS or Lifshitz UV regimes and multi-exponential potentials. Additional perspectives are explored through dimensional reductions of Schrödinger spaces and a waves-on-branes construction, thereby enriching the hvLif landscape and offering pathways toward embedding hvLif holography in string/M-theory. The results provide concrete tools for analyzing stability, entanglement scaling, and potential condensed-matter applications of hvLif spacetimes, while outlining necessary steps to achieve controlled UV/IR completions and interpolating geometries.

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.