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Near-extremal holographic charge correlators

Blaise Goutéraux1,*, David M. Ramirez1,2,†, Mikel Sanchez-Garitaonandia1,‡, and Clément Supiot1,§

  • *Contact author: blaise.gouteraux@polytechnique.edu
  • †Contact author: dr634@cam.ac.uk
  • ‡Contact author: mikel.sanchez@polytechnique.edu
  • §Contact author: clement.supiot@polytechnique.edu
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Phys. Rev. D 114, 086006 – Published 5 October, 2026

DOI: https://doi.org/10.1103/hbf8-wc92

Abstract

We compute analytically the low-temperature charge correlators in near-extremal black holes with a planar horizon and an infrared AdS2×R2 extremal geometry, finding excellent agreement with numerical calculations. By describing consistently the crossover between the hydrodynamic diffusive regime at low frequencies and wave numbers, and the quantum, zero-temperature regime at high frequencies and wave numbers, our analytical result thereby extends significantly the usual regime of applicability of such calculations. We analytically resolve the successive collisions between the diffusive pole and the nonhydrodynamic poles sourced by the infrared AdS2×R2 geometry. We demonstrate that in the T=0 limit, a pair of gapless poles survive with a dispersion relation ω±=−ik2+i(2/3)k4(d4∓iπ+log k2). The nonanalytic contributions arise from the interplay with the branch cut formed by the condensation of the nonhydrodynamic poles. The real part is caused by the “snatching” of one of the nonhydrodynamic poles by the hydrodynamic diffusive pole.

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Phys. Rev. D 114, 086006– Published 5 October, 2026
  • Received 8 October 2025
  • Accepted 11 September 2026
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