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Dispersion relations in non-relativistic two-dimensional materials from quasinormal modes in Hǒrava Gravity

  • Markus GarbisoEmail author
  • Matthias Kaminski
Open Access
Regular Article - Theoretical Physics
  • 34 Downloads

Abstract

We compute dispersion relations of non-hydrodynamic and hydrodynamic modes in a non-relativistic strongly coupled two-dimensional quantum field theory. This is achieved by numerically computing quasinormal modes (QNMs) of a particular analytically known black brane solution to 3+1-dimensional Hǒrava Gravity. Hǒrava Gravity is distinguished from Einstein Gravity by the presence of a scalar field, termed the khronon, defining a preferred time-foliation. Surprisingly, for this black brane solution, the khronon fluctuation numerically decouples from all others, having its own set of purely imaginary eigenfrequencies, for which we provide an analytic expression. All other Hǒrava Gravity QNMs are expressed analytically in terms of QNMs of Einstein Gravity, in units involving the khronon coupling constants and various horizons. Our numerical computation reproduces the analytically known momentum diffusion mode, and extends the analytic expression for the sound modes to a wide range of khronon coupling values. In the eikonal limit (large momentum limit), the analytically known dispersion of QNM frequencies with the momentum is reproduced by our numerics. We provide a parametrization of all QNM frequencies to fourth order in the momentum. We demonstrate perturbative stability in a wide range of coupling constants and momenta.

Keywords

AdS-CFT Correspondence Black Holes Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Supplementary material

13130_2019_11400_MOESM1_ESM.tgz (1.4 mb)
ESM 1 (TGZ 1418 kb)

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of AlabamaTuscaloosaU.S.A.

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