Minding the gap in holographic models of interacting fermions

Abstract

We study the holographic dual of fermions interacting in a Schwarzschild-AdS$_{d+1}$ background via a dipole (Pauli) coupling sourced by a probe gauge field. We find quite generally that a gap forms in the dual operator spectrum as the Pauli coupling is strengthened. Previous investigations have observed this behavior in analogous constructions with Reissner-Nordstr\"om-AdS (RN-AdS$_4$) backgrounds, but the emergence of log-oscillatory behavior in those models' spectra prevented identification of the underlying gapping mechanism. Our model obviates this issue through its modified geometry and traces the gapping mechanism back to the bulk dynamics. We show in general that there is a duality between zeros for large positive values of the coupling and poles in the spectrum for equivalent couplings but with opposite sign as seen recently in the RN-AdS$_4$ background\cite{alsup}. The duality arises from the two possible quantizations for computing the retarded propagator. Coupled with the earlier string results\cite{gauntlett,gubser2} that Fermi surfaces are generally absent from the spectral function, our finding that the Pauli term engineers the gap suggests that the model examined here offers a way of studying non-perturbative physics in fermionic matter at finite density typified by Mott insulating systems.