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 $\hat{I}{¼}_q$ and finite isospin asymmetry. The non-Abelian hydrodynamic description of the charged currents is derived in the presence of an isospin chemical potential $\hat{I}{¼}_3$. The two-point correlators of charged currents are then computed holographically at finite quark and isospin chemical potentials. In the near-extremal hydrodynamic regime, $\ddot{I}‰,k,T,\hat{I}{¼}_3\ll \hat{I}¼\equiv \sqrt{\hat{I}{¼}_q^2+\hat{I}{¼}_3^2}$, 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 $\ddot{I}‰,k\ll T\ll \hat{I}¼$ to the so-called extended hydrodynamic regime $T\ll \ddot{I}‰,k\ll \hat{I}¼$. 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-$\ddot{I}‰$ logarithms. The results are verified through a detailed numerical analysis of the exact correlators and quasi-normal mode spectrum.

70 pages plus appendices