Spectral weight in holographic scaling geometries

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 $\theta$. For any finite $z$ and $\theta$, 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 $\eta = - \theta/z > 0$ held fixed, then the resulting theory is locally quantum critical with an entropy density that vanishes at low temperatures as $s \sim T^\eta$. In these cases the low energy spectral weight at nonzero momentum is not exponentially suppressed, possibly indicating a more fermionic nature of these theories.