Holographic models of non-Fermi liquid metals revisited: An effective field theory approach

Accessing the physics of strongly coupled metals in a controlled way is a challenging problem in theoretical condensed matter physics. In this paper, we revisit the possibility of understanding strongly coupled metals through a holographic duality with a weakly coupled gravitational theory in one higher dimension (i.e., a suitable generalization of the "AdS/CFT duality"). Previous attempts at devising holographic models of strongly coupled metals have suffered from drawbacks; for example, many such models do not even seem to be able to describe a Fermi surface that satisfies Luttinger's theorem, which is ought to be a core requirement in any physically reasonable model of a metal. Here, we propose a radically different approach to constructing holographic models of strongly coupled metals. The idea is that for applications, it should be sufficient to construct a holographic dual of the effective field theory that controls the infrared physics of the metal. We invoke recent paper that has identified a precise criterion for such an effective field theory to be "emergeable" from a continuum ultraviolet (UV) theory at nonzero charge density (or its equivalent in lattice models, namely an incommensurate charge filling). We show that imposing this criterion leads to a holographic model of a strongly coupled metal with physically reasonable properties, including a Fermi surface satisfying Luttinger's theorem. We discuss a possible physical interpretation of our results.