Unitarity bound violation in holography and the instability toward the charge density wave

We study the spectral function of holographic fermions with Pauli term. We find the [Formula: see text]-dependent instability signaled by the tachyonic spectrum ([Formula: see text]-gap) from the [Formula: see text] regime where unitarity is violated. We suggest that this is the instability toward the charge density wave (CDW) based on the similarity of the unitarity violation in conformal field theory (CFT) and the nesting Fermi surface phenomena in weakly interaction system: both of them give divergent enhancement of degree of freedom.