Analytic AC conductivities from holography

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.

arXiv comment10 pages, 3 figures, REVTeX 4.2. v2: extended version; v3: minor corrections, published version. A Mathematica notebook for verifying the solution of the perturbation equation is attached as an ancillary file. A video showing how the poles move and how a branch cut emerges is also attached

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• Dependence of the critical temperature and disorder in holographic superconductors on superfluid density
• The role of torsion in holographic conductivity