Conductivity and quasinormal modes in holographic theories

TL;DR

This paper demonstrates that in holographic field theories, the retarded Green's function for conserved currents can be expressed as a sum over quasinormal modes, linking conductivity to spectral properties through analytical and numerical methods.

Contribution

It introduces a convergent sum representation of Green's functions in holography and derives the asymptotics of quasinormal modes using WKB analysis, providing new analytical insights.

Findings

Sum rule relating zero-frequency conductivity to quasinormal modes

Asymptotic behavior of quasinormal mode frequencies derived

Analytic understanding of spectral density asymptotics

Abstract

We show that in field theories with a holographic dual the retarded Green's function of a conserved current can be represented as a convergent sum over the quasinormal modes. We find that the zero-frequency conductivity is related to the sum over quasinormal modes and their high-frequency asymptotics via a sum rule. We derive the asymptotics of the quasinormal mode frequencies and their residues using the phase-integral (WKB) approach and provide analytic insight into the existing numerical observations concerning the asymptotic behavior of the spectral densities.