Holographic models for theories with hyperscaling violation

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 Schrödinger 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.

Holographic thermalization with Lifshitz scaling and hyperscaling violation

“…By now there exist various holographic dual models for critical points involving Lifschitz scaling and hyperscaling violation [33][34][35][36][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. In the light of the rich scaling structure in the time evolution of entanglement entropy, it is interesting to see how it carries over to systems with Lifshitz scaling and hyperscaling violation.…”

Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography

“…The way we came to this answer is as follows. Using the equations for the linearized perturbation analysis 17 of [89] (setting the parameters a and b defined in [89] equal to zero and truncating the scalar field) we observe by looking at purely radial perturbations around Lifshitz that there are 4 integration constants in the tensor modes, 8 in the vector modes and 4 in the scalar modes (in the radial gauge of [89] one actually encounters 5 parameters but one can be removed by a rescaling of the radial coordinate). One can remove 6 parameters using diffeomorphisms (3 off-shell and another 3 on-shell) leading to 10 parameters.…”

Fermionic field perturbations of a three-dimensional Lifshitz black hole in conformal gravity

“…In order to solve this equation for ψ 2 , we use the integrating factor (z/(1 − z)) −iω/2 and the following property of the hypergeometric function: 47) and from (3.46) we obtain…”

“…Also, by introducing both an Abelian gauge field and a scalar dilaton, spacetimes emerge which, in addition to having an anisotropic scaling exponent z as the Lifshitz metric, have an overall hyperscaling violating factor with hyperscaling exponent η that is not scale invariant; thus, this line element is conformally related to the Lifshitz metric and transforms as ds → λ η/(D−2) ds under the Lifshitz scaling. This spacetime is important in the study of dual field theories with hyperscaling violation [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55], and were also investigated in other gravitational theories [56][57][58]. One important characteristic of black holes is their quasinormal modes (QNMs), which nowadays are of great interest due to the observation of gravitational waves from the merger of two black holes [59].…”