Screening of Coulomb interactions in Holography

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-Nordstr\"om 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.