Flavour current correlators and the non-Abelian hydrodynamic approximation: the charged sector
Flavor-current correlators are studied in strongly-coupled dense (holographic) matter, at finite quark chemical potential $\mu_q$ and finite isospin asymmetry. The non-Abelian hydrodynamic description of the charged currents is derived in the presence of an isospin chemical potential $\mu_3$. The two-point correlators of charged currents are then computed holographically at finite quark and isospin chemical potentials. In the near-extremal hydrodynamic regime, $\omega, k, T, \mu_3 \ll \mu \equiv \sqrt{\mu_q^2+\mu_3^2}$, 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 $\omega, k \ll T \ll \mu$ to the so-called extended hydrodynamic regime $T\ll \omega, k \ll \mu$. 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-$\omega$ logarithms. The results are verified through a detailed numerical analysis of the exact correlators and quasi-normal mode spectrum.