Fermi Surfaces of Holographic Metals

Abstract

One of the most challenging endeavours in theoretical condensed matter physics is solving models of strongly correlated metals. In these systems, the standard techniques from Fermi liquid theory have limited applicability, necessitating new descriptions. One particularly promising approach is known as holographic duality, which conjectures a relation between the seemingly unapproachable physics of strongly coupled quantum field theories and classical gravitational theories in one higher dimension. While successful in many regards, the usual holographic approach for metals fails to incorporate a satisfactory description of a Fermi surface, an indisputably important ingredient for any theory describing a metal. Specifically, any theory of a metal ought to have a Fermi surface that satisfies Luttinger’s theorem. In this thesis, we introduce a holographic model that exhibits the necessary behaviour of metal. Diverging from the typical holographic treatment where all scales are described, we instead assume the dual theory to be an infrared effective field theory. We explore the behaviour of the theory across various temperatures by numerically solving the differential equations of motion for the gravity theory. Motivated by the numerical predictions, we suggest a UV cutoff scale for the theory. We discuss some potential limitations and plausible modifications of the model.