Screening of Coulomb interactions in Holography

Abstract

We introduce Coulomb interactions in the holographic description of strongly interacting systems, by performing a (current-current) double-trace deformation of the boundary theory. In the theory dual to a Reissner-Nordström background, this deformation leads to gapped plasmon modes in the density-density response, as expected from conventional RPA calculations. We further show that by introducing a $(d+1)$-dimensional Coulomb interaction in a boundary theory in $d$ spacetime dimensions, we recover plasmon modes whose dispersion is proportional to $\sqrt{|\mathbf{k}|}$, as observed for example in graphene layers. Moreover, motivated by recent experimental results in layered cuprate high-temperature superconductors, we present a toy model for a layered system consisting of an infinite stack of (spatially) two-dimensional layers, that are coupled only by the long-range Coulomb interaction. This leads to low-energy `acoustic plasmons'. Finally, we compute the optical conductivity of the deformed theory in $d=3+1$, where a logarithmic correction is present and we show how this can be related to the conductivity measured in Dirac and Weyl semimetals.

arXiv comment39 pages, 15 figures; Published version (small changes according to referee's suggestions)

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• Collective modes of polarizable holographic media in magnetic fields
• Chiral magnetic waves in strongly coupled Weyl semimetals
• Holographic fundamental matter in multilayered media
• Coulomb drag between two strange metals
• Screened Coulomb interactions of general macroions with nonzero particle volume
• Holographic D-brane constructions with dynamical gauge fields
• Scheme dependence and instability of double-trace deformations for gauge fields in AdS${}_5$