Analytic AC conductivities from holography

TL;DR

This paper derives exact analytic solutions for holographic AC conductivity at any frequency and temperature, revealing detailed properties of current correlators and their analytic structure in various gravitational backgrounds.

Contribution

It provides the first exact analytic solutions for holographic AC conductivity at arbitrary frequency and temperature, enabling detailed analysis of correlator analyticity.

Findings

Exact solutions for AC conductivity at any frequency and temperature.

Insights into pole movement and branch cut emergence in correlators.

Application to R-current correlator in $ ext{N}=4$ SYM at finite temperature.

Abstract

We find exact, analytic solutions of the holographic AC conductivity at arbitrary frequency $\omega$ and temperature $T$, in contrast to previous works where the AC conductivity was analytically obtained usually at small $\omega$ and $T$. These solutions enable us to study the analyticity properties of the current-current correlator $G(\omega)$ in detail. The first system we study is the AdS$_5$ planar black hole with momentum dissipation, whose extremal limit has an AdS$_2$ factor. Then we study AdS$_4$ and AdS$_5$ Einstein-dilaton systems whose special cases are maximal gauged supergravities. The solutions show how the poles move and how branch cuts emerge as the temperature varies. As a byproduct, we obtain an R-current correlator in $\mathcal{N}=4$ super-Yang-Mills theory on a sphere at finite temperature in the large $N$ and strong coupling limit.