Near-extremal holographic charge correlators

TL;DR

This paper analytically studies charge correlators in near-extremal black holes with an AdS2 geometry, revealing the crossover from hydrodynamic to quantum regimes and detailing pole interactions at low temperatures.

Contribution

It provides an analytical computation of charge correlators in near-extremal black holes, elucidating pole collisions and nonanalytic behaviors at low temperatures.

Findings

Excellent agreement with numerical calculations.

Identification of pole collisions and their effects.

Explicit dispersion relations for gapless poles at zero temperature.

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 $\omega_\pm=-i d_2 k^2-i d_4 k^4-i\tilde d_4 k^4(\pm i\pi+\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.