Holographic Lifshitz fermions and exponentially suppressed spectral weight

The absence of fixed momentum excitations in a theory with Lifshitz scale invariance gives rise to exponential suppression of spectral weight in the low-frequency limit. In the holographic dual, this suppression arises as a consequence of a tunneling barrier that decouples the horizon from the boundary. We compute the spin-1/2 holographic Green's function and show that the form of the barrier is identical to that of the scalar case. We furthermore demonstrate that the suppression factor is universal in the $\hat\omega\to0$ limit where $\hat\omega=\omega/|\vec k|^z$. In particular, it depends only on $\hat\omega$ and the critical exponent $z$, and is independent of scaling dimension and spin.