Spectral weight in holographic scaling geometries

TL;DR

Hartnoll and Shaghoulian investigate low-energy spectral weight in holographic scaling geometries characterized by a dynamical exponent $z$ and hyperscaling violation $\theta$. They show that for any finite $z$ and $\theta$, the low-energy spectral density at finite momentum is exponentially suppressed, consistent with the IR flow toward momentum-space origin and challenging direct identification of hidden Fermi surfaces in the classical bulk. In a double-scaling limit with $z\to\infty$ and $\eta=-\theta/z$ fixed, the theory becomes locally critical with $s\sim T^{\eta}$ and exhibits nonexponentially suppressed finite-momentum spectral weight, with $\text{Im} \; G^R_{J_\perp J_\perp}(\omega,k) \propto \omega^{2\nu_-(k)}$ where $\nu_-(k)$ depends on $k$ and $\eta$. The work clarifies the fermionic character of holographic scaling geometries, showing a stark contrast between finite-$z$ and locally critical regimes, and highlights the need for nonclassical (quantum-gravitational) effects to realize true Fermi-surface physics in these holographic models.

Abstract

We compute the low energy spectral density of transverse currents in theories with holographic duals that exhibit an emergent scaling symmetry characterized by dynamical critical exponent $z$ and hyperscaling violation exponent $θ$. For any finite $z$ and $θ$, the low energy spectral density is exponentially small at nonzero momentum. This indicates that any nonzero momentum low energy excitations of putative hidden Fermi surfaces are not visible in the classical bulk limit. We furthermore show that if the limit $z \to \infty$ is taken with the ratio $η= - θ/z > 0$ held fixed, then the resulting theory is locally quantum critical with an entropy density that vanishes at low temperatures as $s \sim T^η$. In these cases the low energy spectral weight at nonzero momentum is not exponentially suppressed, possibly indicating a more fermionic nature of these theories.