Fermi surfaces and gauge-gravity duality

TL;DR

This paper reviews various zero-temperature phases of compressible quantum matter with Fermi surfaces, highlighting their properties, models, and connections to gauge-gravity duality, including both Fermi liquid and non-Fermi liquid behaviors.

Contribution

It provides a unified overview of compressible phases with Fermi surfaces, linking condensed matter models to gauge-gravity duality frameworks and exploring their diverse singularities.

Findings

Fermi surfaces obey the Luttinger theorem relating volume to charge Q

Existence of both Fermi liquid and non-Fermi liquid Fermi surfaces

Compressible phases are present in models relevant to condensed matter and gauge theories

Abstract

We give a unified overview of the zero temperature phases of compressible quantum matter: i.e. phases in which the expectation value of a globally conserved U(1) density, Q, varies smoothly as a function of parameters. Provided the global U(1) and translational symmetries are unbroken, such phases are expected to have Fermi surfaces, and the Luttinger theorem relates the volumes enclosed by these Fermi surfaces to <Q>. We survey models of interacting bosons and/or fermions and/or gauge fields which realize such phases. Some phases have Fermi surfaces with the singularities of Landau's Fermi liquid theory, while other Fermi surfaces have non-Fermi liquid singularities. Compressible phases found in models applicable to condensed matter systems are argued to also be present in models obtained by applying chemical potentials (and other deformations allowed by the residual symmetry at non-zero chemical potential) to the paradigmic supersymmetric gauge theories underlying gauge-gravity duality: the ABJM model in spatial dimension d=2, and the N=4 SYM theory in d=3.