Electron stars for holographic metallic criticality

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 $Ad{S}_{4}$ 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.