Momentum analyticity of transverse polarization tensor in the normal phase of a holographic superconductor

We explore the momentum analyticity of the static transverse polarization tensor of a 2+1 dimensional holographic superconductor in its normal phase, aiming at finding the holographic counterpart of the singularities underlying the friedel oscillations of an ordinary field theory. we prove that the polarization tensor is a meromorphic function with an infinite number of poles located on the complex momentum plane off real axis. with the aid of the wkb approximation these poles are found to lies asymptotically along two straight lines parallel to the imaginary axis for a large momentum magnitude. the similarity between the holographic green’s function and that of an weakly coupled ordinary field theory (e.g., 2+1 dimensional qed) regarding the location of the momentum singularities offers further support to the validity of the gauge/gravity duality.