Hydrodynamic excitations from chiral kinetic theory and the hydrodynamic frames
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Springer
Received: December 31, 2017 Accepted: February 1, 2018 Published: March 30, 2018
Navid Abbasi,a Farid Taghinavaza and Kiarash Naderib a
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran b Department of Physics, Sharif University of Technology, Azadi Ave, Tehran, Iran
E-mail: [email protected], [email protected], [email protected] Abstract: In the framework of chiral kinetic theory (CKT), we consider a system of rightand left-handed Weyl fermions out of thermal equilibrium in a homogeneous weak magnetic field. We show that the Lorentz invariance implies a modification in the definition of the momentum current in the phase space, compared to the case in which the system is in global equilibrium. Using this modified momentum current, we derive the linearized conservation equations from the kinetic equation up to second order in the derivative expansion. It turns out 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 be transformed 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 the difference between the right- and left-handed charges susceptibility. We then compute the chiral transport coefficients in a system of non-Abelian chiral fermions in the no-drag frame and by making the above boost, obtain the well-known transport coeffiecients of the system in the LL frame. Finally by using the idea of boost, we reproduce the AdS/CFT result for the chiral drag force exerted on a quark at rest in the rest frame of the fluid, without performing any holographic computations. Keywords: AdS-CFT Correspondence, Holography and quark-gluon plasmas ArXiv ePrint: 1712.06175
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)191
JHEP03(2018)191
Hydrodynamic excitations from chiral kinetic theory and the hydrodynamic frames
Contents 2
2 Chiral kinetic theory and its new modification 2.1 Global equilibrium state 2.2 Local equilibrium state 2.3 Modifying the momentum current
5 7 8 9
3 Perturbative solution for the kinetic equation 3.1 Conservation equations 3.1.1 Charge conservation 3.1.2 Energy conservation 3.1.3 Momentum conservation 3.2 Hydro modes
10 10 11 12 13 14
4 Review of hydro modes from hydrodynamics in Landau-Lifshitz frame
17
5 Modes in Lab frame from those in Lanadau-Lifshitz frame
20
6 Lab frame is a no-drag frame 6.1 No-drag frame for a system of non-abelian fermions 6.2 Reproducing the results of Neiman-Oz by boost
23 24 29
7 The general form of chiral drag force in the Landau-Lifshitz frame: comparison with the holography result 30 7.1 Chiral drag force in the Landau-Lifshitz frame 30 7.2 Comparison with the AdS/CFT result 32 8 Summary, conclusion and outlook
34
A Supplementary material A.1 Conservation equations i
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