Hydrodynamic Excitations from Chiral Kinetic Theory and the Hydrodynamic Frames

摘要

In the framework of chiral kinetic theory (CKT), we consider a system ofright- and left-handed Weyl fermions out of thermal equilibrium in ahomogeneous weak magnetic field. We show that the Lorentz invariance implies amodification in the definition of the momentum current in the phase space,compared to the case in which the system is in global equilibrium. Using thismodified momentum current, we derive the linearized conservation equations fromthe kinetic equation up to second order in the derivative expansion. It turnsout that the eigenmodes of these equations, namely the hydrodynamic modes,differ from those obtained from the hydrodynamic in the Landau-Lifshitz (LL)frame at the same order. We show that the modes of the former case may betransformed to the corresponding modes in the latter case by a global boost.The velocity of the boost is proportional to the magnetic field as well as thedifference between the right- and left-handed charges susceptibility. We thencompute the chiral transport coefficients in a system of non-Abelian chiralfermions in the no-drag frame and by making the above boost, obtain thewell-known transport coeffiecients of the system in the LL frame. Finally byusing the idea of boost, we reproduce the AdS/CFT result for the chiral dragforce exerted on a quark at rest in the rest frame of the fluid, withoutperforming any holographic computations.