Abstract
In the framework of chiral kinetic theory (CKT), we consider a system of right-and 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Vilenkin, Equilibrium Parity Violating Current In A Magnetic Field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].
H.B. Nielsen and M. Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B 130 (1983) 389 [INSPIRE].
D.E. Kharzeev and H.-U. Yee, Chiral Magnetic Wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [INSPIRE].
Y. Burnier, D.E. Kharzeev, J. Liao and H.-U. Yee, Chiral magnetic wave at finite baryon density and the electric quadrupole moment of quark-gluon plasma in heavy ion collisions, Phys. Rev. Lett. 107 (2011) 052303 [arXiv:1103.1307] [INSPIRE].
STAR collaboration, L. Adamczyk et al., Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions, Phys. Rev. Lett. 114 (2015) 252302 [arXiv:1504.02175] [INSPIRE].
ALICE collaboration, Charge-dependent anisotropic flow studies and the search for the Chiral Magnetic Wave in ALICE, Nucl. Phys. A 931 (2014) 981 [arXiv:1408.1043] [INSPIRE].
D.T. Son and B.Z. Spivak, Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals, Phys. Rev. B 88 (2013) 104412 [arXiv:1206.1627] [INSPIRE].
X. Huang et al., Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs, Phys. Rev. X 5 (2015) 031023 [arXiv:1503.01304] [INSPIRE].
H. Li et al., Negative magnetoresistance in Dirac semimetal Cd 3 As 2, Nature Commun. 7 (2016) 10301 [arXiv:1507.06470].
A. Vilenkin, Macroscopic Parity Violating Effects: Neutrino Fluxes From Rotating Black Holes And In Rotating Thermal Radiation, Phys. Rev. D 20 (1979) 1807 [INSPIRE].
P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya and M.I. Polikarpov, Numerical evidence of chiral magnetic effect in lattice gauge theory, Phys. Rev. D 80 (2009) 054503 [arXiv:0907.0494] [INSPIRE].
J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surowka, Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
J. Gooth et al., Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP, Nature 547 (2017) 324 [arXiv:1703.10682] [INSPIRE].
D.T. Son and N. Yamamoto, Berry Curvature, Triangle Anomalies and the Chiral Magnetic Effect in Fermi Liquids, Phys. Rev. Lett. 109 (2012) 181602 [arXiv:1203.2697] [INSPIRE].
M.A. Stephanov and Y. Yin, Chiral Kinetic Theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [INSPIRE].
M.A. Stephanov, H.-U. Yee and Y. Yin, Collective modes of chiral kinetic theory in a magnetic field, Phys. Rev. D 91 (2015) 125014 [arXiv:1501.00222] [INSPIRE].
J.-Y. Chen, D.T. Son, M.A. Stephanov, H.-U. Yee and Y. Yin, Lorentz Invariance in Chiral Kinetic Theory, Phys. Rev. Lett. 113 (2014) 182302 [arXiv:1404.5963] [INSPIRE].
D.T. Son and N. Yamamoto, Kinetic theory with Berry curvature from quantum field theories, Phys. Rev. D 87 (2013) 085016 [arXiv:1210.8158] [INSPIRE].
J.-Y. Chen, D.T. Son and M.A. Stephanov, Collisions in Chiral Kinetic Theory, Phys. Rev. Lett. 115 (2015) 021601 [arXiv:1502.06966] [INSPIRE].
N. Yamamoto, Chiral Alfvén Wave in Anomalous Hydrodynamics, Phys. Rev. Lett. 115 (2015) 141601 [arXiv:1505.05444] [INSPIRE].
N. Abbasi, A. Davody, K. Hejazi and Z. Rezaei, Hydrodynamic Waves in an Anomalous Charged Fluid, Phys. Lett. B 762 (2016) 23 [arXiv:1509.08878] [INSPIRE].
N. Abbasi, D. Allahbakhshi, A. Davody and S.F. Taghavi, Hydrodynamic excitations in hot QCD plasma, Phys. Rev. D 96 (2017) 126002 [arXiv:1612.08614] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
K. Landsteiner, Notes on Anomaly Induced Transport, Acta Phys. Polon. B 47 (2016) 2617 [arXiv:1610.04413] [INSPIRE].
M.A. Stephanov and H.-U. Yee, No-Drag Frame for Anomalous Chiral Fluid, Phys. Rev. Lett. 116 (2016) 122302 [arXiv:1508.02396] [INSPIRE].
Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].
J.-H. Gao, Z.-T. Liang, S. Pu, Q. Wang and X.-N. Wang, Chiral Anomaly and Local Polarization Effect from Quantum Kinetic Approach, Phys. Rev. Lett. 109 (2012) 232301 [arXiv:1203.0725] [INSPIRE].
S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].
C.P. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L.G. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
K. Rajagopal and A.V. Sadofyev, Chiral drag force, JHEP 10 (2015) 018 [arXiv:1505.07379] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous Transport from Kubo Formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808] [INSPIRE].
D. Frenklakh, Chiral heat wave and mixed waves in kinetic theory, Phys. Rev. D 94 (2016) 116010 [arXiv:1603.08971] [INSPIRE].
M.N. Chernodub, Chiral Heat Wave and mixing of Magnetic, Vortical and Heat waves in chiral media, JHEP 01 (2016) 100 [arXiv:1509.01245] [INSPIRE].
D.E. Kharzeev and H.-U. Yee, Anomalies and time reversal invariance in relativistic hydrodynamics: the second order and higher dimensional formulations, Phys. Rev. D 84 (2011) 045025 [arXiv:1105.6360] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A Theory of first order dissipative superfluid dynamics, JHEP 05 (2014) 147 [arXiv:1105.3733] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational Anomaly and Transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
P.M. Chesler and L.G. Yaffe, The Stress-energy tensor of a quark moving through a strongly-coupled N = 4 supersymmetric Yang-Mills plasma: Comparing hydrodynamics and AdS/CFT, Phys. Rev. D 78 (2008) 045013 [arXiv:0712.0050] [INSPIRE].
N. Abbasi and A. Davody, Moving Quark in a Viscous Fluid, JHEP 06 (2012) 065 [arXiv:1202.2737] [INSPIRE].
N. Abbasi and A. Davody, The Energy Loss of a Heavy Quark Moving Through a General Fluid Dynamical Flow, JHEP 12 (2013) 026 [arXiv:1310.4105] [INSPIRE].
C.P. Herzog, Energy Loss of Heavy Quarks from Asymptotically AdS Geometries, JHEP 09 (2006) 032 [hep-th/0605191] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, Cambridge University Press, Cambridge U.K. (2014) [ISBN: 9781139136747] [arXiv:1101.0618] [INSPIRE].
M. Lekaveckas and K. Rajagopal, Effects of Fluid Velocity Gradients on Heavy Quark Energy Loss, JHEP 02 (2014) 068 [arXiv:1311.5577] [INSPIRE].
T. Kalaydzhyan and E. Murchikova, Thermal chiral vortical and magnetic waves: new excitation modes in chiral fluids, Nucl. Phys. B 919 (2017) 173 [arXiv:1609.00024] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Parity-Violating Hydrodynamics in 2 + 1 Dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [INSPIRE].
M. Ammon, M. Kaminski, R. Koirala, J. Leiber and J. Wu, Quasinormal modes of charged magnetic black branes & chiral magnetic transport, JHEP 04 (2017) 067 [arXiv:1701.05565] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1712.06175
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Abbasi, N., Taghinavaz, F. & Naderi, K. Hydrodynamic excitations from chiral kinetic theory and the hydrodynamic frames. J. High Energ. Phys. 2018, 191 (2018). https://doi.org/10.1007/JHEP03(2018)191
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2018)191