Spectral probes of the holographic Fermi groundstate: dialing between the electron star and AdS Dirac hair

TL;DR

This paper explores the connection between electron star and Dirac hair solutions in holography, showing they are limits of a free charged Fermi gas in AdS, and investigates how the number of Fermi surfaces varies with constituent fermions.

Contribution

It introduces a parameterized family of holographic fermion spectral functions interpolating between electron star and Dirac hair solutions, revealing how Fermi surface structures change with constituent fermion number.

Findings

Number of Fermi surfaces decreases as constituent fermions decrease.

Electron star limit corresponds to infinite constituents, Dirac hair to a single constituent.

Spectral functions can be tuned to interpolate between the two limits.

Abstract

We argue that the electron star and the AdS Dirac hair solution are two limits of the free charged Fermi gas in AdS. Spectral functions of holographic duals to probe fermions in the background of electron stars have a free parameter that quantifies the number of constituent fermions that make up the charge and energy density characterizing the electron star solution. The strict electron star limit takes this number to be infinite. The Dirac hair solution is the limit where this number is unity. This is evident in the behavior of the distribution of holographically dual Fermi surfaces. As we decrease the number of constituents in a fixed electron star background the number of Fermi surfaces also decreases. An improved holographic Fermi groundstate should be a configuration that shares the qualitative properties of both limits.