  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.
