Plasmons in Holographic Ersatz Fermi Liquids

We solve an infrared effective holographic model of a non-Fermi liquid at finite temperature that satisfies Luttinger's theorem and incorporates long-range Coulomb interactions. Motivated by the absence of a Luttinger-counting Fermi surface in standard Reissner-Nordstrom holographic metals, we consider a Maxwell-Chern-Simons theory in a static anti-de Sitter-Schwarzschild background, coupled to an LU(1) gauge field rather than a conventional U(1) gauge field. By an appropriate choice of boundary conditions, we obtain a damped collective plasmon mode whose plasma frequency scales as predicted by Luttinger's theorem. We further analyze the density-density correlator in the absence of long-range Coulomb interactions and identify a contribution consistent with a Lindhard-like continuum.