Minding the Gap in N=4 Super-Yang-Mills

We analyze fermionic response in the geometry holographically dual to zero-temperature N=4 Super-Yang-Mills theory with two equal nonvanishing chemical potentials, which is characterized by a singular horizon and zero ground state entropy. We show that fermionic fluctuations are completely stable within a gap in energy around a Fermi surface singularity, beyond which non-Fermi liquid behavior returns. This gap disappears abruptly once the final charge is turned on, and is associated to a discontinuity in the corresponding chemical potential. We also show that the singular near-horizon geometry lifts to a smooth AdS_3 x R^3, and interpret the gap as a region where the quasiparticle momentum is spacelike in six dimensions due to the momentum component in the Kaluza-Klein direction, corresponding to the final charge.