Flavour current correlators and the non-Abelian hydrodynamic approximation: the charged sector

Abstract

Flavor-current correlators are studied in strongly-coupled dense (holographic) matter, at finite quark chemical potential $μ_q$ and finite isospin asymmetry. The non-Abelian hydrodynamic description of the charged currents is derived in the presence of an isospin chemical potential $μ_3$. The two-point correlators of charged currents are then computed holographically at finite quark and isospin chemical potentials. In the near-extremal hydrodynamic regime, $ω, k, T, μ_3 \ll μ\equiv \sqrt{μ_q^2+μ_3^2}$, relevant for cold strongly coupled matter, the IR properties of the correlators are studied. It is shown that in this regime, the correlators agree with the non-Abelian hydrodynamic predictions. Therefore, the traditional regime of validity of standard hydrodynamics extends beyond $ω, k \ll T \ll μ$ to the so-called extended hydrodynamic regime $T\ll ω, k \ll μ$. The holographic product formula is applied to the present non-Abelian system, and is used to propose an extended hydrodynamic approximation capturing both hydrodynamic-like poles and the leading effect of AdS$_2$ poles, by resumming the low-$ω$ logarithms. The results are verified through a detailed numerical analysis of the exact correlators and quasi-normal mode spectrum.