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{left|mathbf{k}right|} , 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.