NLO corrections to charged-current correlators near extremality: non-Abelian hydrodynamics meets AdS$_2$

Abstract

We analytically compute the longitudinal charged-current correlator in a near-extremal holographic plasma with quark and isospin chemical potentials, $μ_q$ and $μ_3$ respectively. To this end, we study fluctuations of gauge fields around a low-temperature AdS$_5$ Reissner-Nordström black hole charged both under the quark number and the isospin. The result is obtained at next-to-leading order in a hydrodynamic expansion where apart from the temperature and isospin chemical potential, the frequency and momenta are small compared to the quark chemical potential, $ω,k,T,μ_3\llμ_q$. This approach captures the interplay between the hydrodynamic-like pole and the tower of infrared modes produced by the AdS$_2$ throat controlling the geometry of the black hole near extremality. At zero isospin chemical potential, the resulting quasinormal-mode formula reproduces the collision of the diffusive pole with the infrared spectrum, while the finite isospin chemical potential lifts this collision. The analytic spectrum agrees precisely with the full numerical results. The next-to-leading-order correlator also substantially improves the spectral function beyond the standard hydrodynamic regime $ω,k,μ_3\ll T$, extending the agreement with numerics to larger frequencies and momenta.