A model of a Fermi liquid using gauge-gravity duality

TL;DR

This paper models the transition from a conformal critical point to a confining Fermi liquid using gauge-gravity duality, connecting holographic geometry with Fermi liquid properties.

Contribution

It introduces a holographic model capturing the crossover from conformal to Fermi liquid behavior, deriving the Luttinger relation from bulk Gauss's Law.

Findings

Luttinger relation derived from holography

Explicit Fermi liquid solution with hard-wall boundary conditions

Low energy modes consistent with Landau Fermi liquid theory

Abstract

We use gauge-gravity duality to model the crossover from a conformal critical point to a confining Fermi liquid, driven by a change in fermion density. The short-distance conformal physics is represented by an anti-de Sitter geometry, which terminates into a confining state along the emergent spatial direction. The Luttinger relation, relating the area enclosed by the Fermi surfaces to the fermion density, is shown to follow from Gauss's Law for the bulk electric field. We argue that all low energy modes are consistent with Landau's Fermi liquid theory. An explicit solution is obtained for the Fermi liquid for the case of hard-wall boundary conditions in the infrared.