Continuum effective field theories, gravity, and holography

We examine effective field theories (EFTs) with a continuum sector in the presence of gravity. We first explain, via arguments based on central charge and species scale, that an EFT with a free continuum cannot consistently couple to standard (i.e., 4D Einstein) gravity. It follows that EFTs with a free or nearly free continuum must have either a finite number of degrees of freedom or nonstandard gravity. The latter claim is realized for holographically defined continuum models. We demonstrate this by computing the deviations from standard gravity in a specific 5D scalar-gravity system that gives rise to a gapped continuum (i.e., the linear dilaton background). We find an R-2 deviation from the Newtonian potential. At finite temperature, we find an energy density with matterlike behavior in the brane Friedmann equation, holographically induced from the bulk geometry. Thus, remarkably, a braneworld living in the linear dilaton background automatically contains dark matter. We also present a slightly more evolved asymptotically AdS linear dilaton model, for which the deviations exhibit a transition between AdS and linear dilaton behaviors.