Stellar spectroscopy: Fermions and holographic Lifshitz criticality

TL;DR

This paper analyzes the Green's function of fermionic operators in holographic electron star models, revealing multiple Fermi surfaces, their charge distribution, and the impact of Lifshitz criticality on fermionic excitations and conductivity.

Contribution

It provides a detailed computation of the fermionic Green's function in electron star backgrounds, highlighting the structure of Fermi surfaces and their relation to Lifshitz scaling.

Findings

Multiple closely spaced Fermi surfaces consistent with charge density

Long-lived excitations below critical dispersion relation

Strong dissipation of quasiparticles beyond critical energy scale

Abstract

Electron stars are fluids of charged fermions in Anti-de Sitter spacetime. They are candidate holographic duals for gauge theories at finite charge density and exhibit emergent Lifshitz scaling at low energies. This paper computes in detail the field theory Green's function G^R(w,k) of the gauge-invariant fermionic operators making up the star. The Green's function contains a large number of closely spaced Fermi surfaces, the volumes of which add up to the total charge density in accordance with the Luttinger count. Excitations of the Fermi surfaces are long lived for w <~ k^z. Beyond w ~ k^z the fermionic quasiparticles dissipate strongly into the critical Lifshitz sector. Fermions near this critical dispersion relation give interesting contributions to the optical conductivity.