Holographic zeros and poles from apparent singularities

Abstract: We study general holographic fluctuation equations with apparent singularities, and the associated spectral functions. We consider the regime where an apparent singularity approaches the boundary, for which the near-boundary behavior of solutions can be determined via an inner/outer matching type of calculation. Depending on properties of the equation, we find that the merging of an apparent singularity with the boundary may generate either a zero or a pole for the corresponding spectral function. Our results also indicate that the recently introduced holographic product formula still applies in the presence of apparent singularities.