Momentum analyticity of the holographic electric polarizability in 2+1 dimensions

TL;DR

This paper proves that the holographic electric polarization in a 2+1 dimensional field theory dual to Einstein-Maxwell in AdS4 is a meromorphic function, analyzing its pole distribution and comparing with weak-coupling QED models.

Contribution

It analytically characterizes the momentum analyticity and pole distribution of the holographic polarization in a specific AdS/CFT setup, providing new insights into its complex structure.

Findings

Polarization is a meromorphic function in complex momentum plane.

Poles are asymptotically distributed along two lines parallel to the imaginary axis.

Comparison with weak-coupling QED models reveals similarities and differences.

Abstract

The static electric polarization of a holographic field theory dual to the Einstein-Maxwell theory in the background of $AdS_4$ with a Reissner-Nordst\"{o}m (AdS-RN) black hole is investigated. We prove that the holographic polarization is a meromorphic functions in complex momentum plane and locate analytically the asymptotic distribution of the poles along two straight lines parallel to the imaginary axis for a large momentum magnitude. The results are compared with the numerical result on Friedel-like poles of the same holographic model reported in the literature and with the momentum singularities of the one-loop polarization in weak-coupling spinor QED$_3$ and scalar QED$_3$ with the similarities and differences discussed.