Electron stars for holographic metallic criticality

TL;DR

This paper introduces electron stars as holographic duals for strongly interacting fermionic systems at finite density, revealing emergent Lifshitz scaling and analyzing their electrical properties.

Contribution

It demonstrates how electron stars develop IR Lifshitz scaling due to interactions, providing a new gravitational model for finite density fermionic matter.

Findings

Electron stars exhibit emergent Lifshitz scaling at low energies.

The IR scaling results from interactions between quantum critical modes and fermions.

Electrical conductivity of electron stars can be computed from the model.

Abstract

We refer to the ground state of a gravitating, charged ideal fluid of fermions held at a finite chemical potential as an `electron star'. In a holographic setting, electron stars are candidate gravity duals for strongly interacting finite fermion density systems. We show how electron stars develop an emergent Lifshitz scaling at low energies. This IR scaling region is a consequence of the two way interaction between emergent quantum critical bosonic modes and the finite density of fermions. By integrating from the IR region to an asymptotically AdS_4 spacetime, we compute basic properties of the electron stars, including their electrical conductivity. We emphasize the challenge of connecting UV and IR physics in strongly interacting finite density systems.