Near-extremal holographic charge correlators
Blaise Goutéraux, David M. Ramirez, Mikel Sanchez-Garitaonandia, Clément Supiot
TL;DR
The paper analyzes low-temperature charge dynamics in near-extremal planar black holes with an AdS$_2\times\mathbb{R}^2$ IR region, deriving an analytic expression for the current-current retarded Green's function $G^R_{xx}$ in the regime $\omega\sim k^2\sim T$. By solving a matched outer/inner (AdS$_4$/$AdS_2$) problem, it uncovers a sequence of pole collisions between the hydrodynamic diffusive mode and infrared poles, and in the zero-temperature limit identifies a pair of gapless poles with a nontrivial $\mathcal{O}(k^4)$ dispersion plus nonanalytic $\log k$ contributions from the IR branch cut. The real part of the dispersion arises from the snatching of a non-hydrodynamic pole by the diffusive mode, revealing a rich IR-sensitive structure that connects hydrodynamic and quantum regimes. The work provides a concrete holographic model with axions, presents detailed matching calculations, and discusses extensions to backreacted geometries and effective actions (including the Schwarzian) and future quantum-corrected analyses.
Abstract
We analytically compute the low-temperature charge correlators in near-extremal black holes with a planar horizon and an infrared $\mathrm{AdS}_2\times \Bbb{R}^2$ extremal geometry, finding excellent agreement with numerical calculations. The analytical result consistently describes the crossover between the hydrodynamic diffusive regime at low frequencies and wavenumbers, and the quantum, zero-temperature regime at high frequencies and wavenumbers. We analytically resolve the successive collisions between the diffusive pole and the non-hydrodynamic poles sourced by the infrared $\mathrm{AdS}_2\times \Bbb{R}^2$ geometry. We demonstrate that in the $T=0$ limit, a pair of gapless poles survive with a dispersion relation $ω_\pm=-i d_2 k^2-i d_4 k^4-i\tilde d_4 k^4(\pm iπ+\log k^2) $. The nonanalytic contributions arise from the interplay with the branch cut formed by the condensation of the non-hydrodynamic poles. The real part is caused by the `snatching' of one of the non-hydrodynamic poles by the hydrodynamic diffusive pole.