Emerging Fermi liquids from regulated Quantum Electron Stars

Abstract

We construct a fully quantum zero-temperature electron star in a soft-wall regulated anti-de-Sitter Einstein-Maxwell-Dirac theory that is thermodynamically stable compared to the Reissner-Nordstr\"{o}m black hole. The soft wall only acts on the effective mass of the fermionic degrees of freedom, and allows for a controlled fully backreacted solution. The star is holographically dual to an RG flow where a gapped Fermi liquid starts to emerge from a UV CFT, but decouples again once the effective energy scale becomes lower than the the gap of the fermionic degrees of freedom. The RG flow then returns to a non-trivial strongly coupled relativistic fixed point with a holographic dual. Our regulated quantum electron star is thus the fermionic analogue of the Horowitz-Roberts-Gubser-Rocha AdS-to-AdS domain wall solution for the holographic superconductor.