Stellar spectroscopy: Fermions and holographic Lifshitz criticality

TL;DR

The paper analyzes gauge-invariant fermionic operators in holographic electron-star backgrounds, where a bulk fluid of charged fermions yields an IR Lifshitz geometry. Using a WKB Dirac equation treatment, the authors identify a dense spectrum of boundary Fermi surfaces whose volumes add up to the total charge, satisfying a 2+1D Luttinger count despite non-Fermi-liquid behavior. A crucial finding is the dispersion-driven crossover at $\\omega \\sim k^z$: for $\\omega \\lesssim k^z$ excitations are long-lived, while for $\\omega \\gtrsim k^z$ they dissipate into the Lifshitz sector, with implications for transport such as optical conductivity. The work also analyzes special limits (near the Fermi surface extremum and small-star Lifshitz cores), deriving analytic expressions and demonstrating a rich structure of poles, branch cuts, and dispersion relations that encode the interplay between bulk Fermi surfaces and the emergent critical sector.

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.

Figures (9)

• Figure 1: A nonzero charge density is imposed as a UV boundary condition. The IR physics is to be determined by solving the bulk equations of motion.
• Figure 2: Illustrative radial dependence of the Schrödinger potential when $\omega = 0$. The thick green line denotes oscillatory regions. To the left is the horizon while the boundary is to the right at $r \to 0$.
• Figure 3: Illustrative radial dependence of the Schrödinger potential (with $z>1$) in the three possible cases at small nonzero frequency. The thick green line denotes oscillatory regions. To the left is the horizon while the boundary is to the right at $r \to 0$.
• Figure 4: Schematic dependence of the dual field theory fermion spectral density as a function of $\omega$ and $k$ for $z>1$. Red lines denote the dispersion of sharp Fermi surface poles. In case I there are no low energy excitations because all the available Fermi momenta are too far away. In case III there are no well defined excitations because the Fermi surface has become unstable towards dissipation into the critical Lifshitz sector.
• Figure 5: Exponent of the residue of the Fermi surface poles as a function of Fermi momentum (in units of the charge density). Left hand plot has $\hat{m} = 0.3$ for all curves while the right hand plot has $z=2$ for all curves. The plots show that Fermi surfaces near the maximal Fermi momentum have exponentially small spectral weight compared the other poles.