Momentum Analyticity of Transverse Polarization Tensor in the Normal Phase of a Holographic Superconductor

TL;DR

This paper investigates the momentum analyticity of the transverse polarization tensor in a 2+1D holographic superconductor's normal phase, revealing a meromorphic structure with poles aligned asymptotically along lines parallel to the imaginary axis, supporting gauge/gravity duality.

Contribution

It demonstrates that the polarization tensor is a meromorphic function with an infinite set of poles, providing insight into the holographic counterpart of Friedel oscillations.

Findings

Poles are located off the real axis in the complex momentum plane.

Poles asymptotically align along lines parallel to the imaginary axis.

The structure supports the similarity between holographic Green's functions and weakly coupled field theories.

Abstract

We explore the momentum analyticity of the static transverse polarization tensor of a 2+1 dimensional holographic superconductor in its normal phase with a nonzero chemical potential, aiming at finding the holographic counterpart of the singularities underlying the Friedel-like 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.