Abstract
We develop covariant chiral kinetic theory with Landau level basis. We use it to investigate a magnetized plasma with a transverse electric field and a steady vorticity as perturbations. After taking into account vacuum shift in the latter case, we find the resulting current and stress tensor in both cases can be matched consistently with constitutive equations of magnetohydrodynamics. We find the solution in the vorticity case contains both shifts in temperature and chemical potential as well as excitations of the lowest Landau level states. The solution gives rise to an vector charge density and axial current density. The vacuum parts coming from both shifts and excitations agree with previous studies and the medium parts coming entirely from excitations leads to a new contribution to vector charge and axial current density consistent with standard chiral vortical effect.
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References
A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].
D. Kharzeev, Parity violation in hot QCD: why it can happen, and how to look for it, Phys. Lett. B 633 (2006) 260 [hep-ph/0406125] [INSPIRE].
D. Kharzeev and A. Zhitnitsky, Charge separation induced by P-odd bubbles in QCD matter, Nucl. Phys. A 797 (2007) 67 [arXiv:0706.1026] [INSPIRE].
K. Fukushima, D. E. Kharzeev and H. J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
D. T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
Y. Neiman and Y. Oz, Relativistic hydrodynamics with general anomalous charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].
A. Vilenkin, Quantum field theory at finite temperature in a rotating system, Phys. Rev. D 21 (1980) 2260 [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].
K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
K. Hattori and Y. Yin, Charge redistribution from anomalous magnetovorticity coupling, Phys. Rev. Lett. 117 (2016) 152002 [arXiv:1607.01513] [INSPIRE].
Y. Liu and I. Zahed, Pion condensation by rotation in a magnetic field, Phys. Rev. Lett. 120 (2018) 032001 [arXiv:1711.08354] [INSPIRE].
H.-L. Chen, K. Fukushima, X.-G. Huang and K. Mameda, Analogy between rotation and density for Dirac fermions in a magnetic field, Phys. Rev. D 93 (2016) 104052 [arXiv:1512.08974] [INSPIRE].
G. Cao and L. He, Rotation induced charged pion condensation in a strong magnetic field: a Nambu-Jona-Lasino model study, Phys. Rev. D 100 (2019) 094015 [arXiv:1910.02728] [INSPIRE].
H.-L. Chen, X.-G. Huang and K. Mameda, Do charged pions condense in a magnetic field with rotation?, arXiv:1910.02700 [INSPIRE].
Y. Bu and S. Lin, Magneto-vortical effect in strongly coupled plasma, Eur. Phys. J. C 80 (2020) 401 [arXiv:1912.11277] [INSPIRE].
K. Fukushima, T. Shimazaki and L. Wang, Mode decomposed chiral magnetic effect and rotating fermions, Phys. Rev. D 102 (2020) 014045 [arXiv:2004.05852] [INSPIRE].
P. Kovtun, Thermodynamics of polarized relativistic matter, JHEP 07 (2016) 028 [arXiv:1606.01226] [INSPIRE].
J. Hernandez and P. Kovtun, Relativistic magnetohydrodynamics, JHEP 05 (2017) 001 [arXiv:1703.08757] [INSPIRE].
S. Grozdanov, D. M. Hofman and N. Iqbal, Generalized global symmetries and dissipative magnetohydrodynamics, Phys. Rev. D 95 (2017) 096003 [arXiv:1610.07392] [INSPIRE].
M. Hongo and K. Hattori, Revisiting relativistic magnetohydrodynamics from quantum electrodynamics, JHEP 02 (2021) 011 [arXiv:2005.10239] [INSPIRE].
K. Hattori, Y. Hirono, H.-U. Yee and Y. Yin, MagnetoHydrodynamics with chiral anomaly: phases of collective excitations and instabilities, Phys. Rev. D 100 (2019) 065023 [arXiv:1711.08450] [INSPIRE].
X.-G. Huang, A. Sedrakian and D. H. Rischke, Kubo formulae for relativistic fluids in strong magnetic fields, Annals Phys. 326 (2011) 3075 [arXiv:1108.0602] [INSPIRE].
S. I. Finazzo, R. Critelli, R. Rougemont and J. Noronha, Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields, Phys. Rev. D 94 (2016) 054020 [Erratum ibid. 96 (2017) 019903] [arXiv:1605.06061] [INSPIRE].
M. Buzzegoli, Thermodynamic equilibrium of massless fermions with vorticity, chirality and electromagnetic field, arXiv:2011.09974 [INSPIRE].
S. Lin and L. Yang, Chiral kinetic theory from Landau level basis, Phys. Rev. D 101 (2020) 034006 [arXiv:1909.11514] [INSPIRE].
H. Gao, Z. Mo and S. Lin, Photon self-energy in a magnetized chiral plasma from kinetic theory, Phys. Rev. D 102 (2020) 014011 [arXiv:2002.07959] [INSPIRE].
K. Hattori, S. Li, D. Satow and H.-U. Yee, Longitudinal conductivity in strong magnetic field in perturbative QCD: complete leading order, Phys. Rev. D 95 (2017) 076008 [arXiv:1610.06839] [INSPIRE].
X.-L. Sheng, D. H. Rischke, D. Vasak and Q. Wang, Wigner functions for fermions in strong magnetic fields, Eur. Phys. J. A 54 (2018) 21 [arXiv:1707.01388] [INSPIRE].
K. Fukushima and Y. Hidaka, Resummation for the field-theoretical derivation of the negative magnetoresistance, JHEP 04 (2020) 162 [arXiv:1906.02683] [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].
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].
M. A. Stephanov and Y. Yin, Chiral kinetic theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [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. Pu, J.-H. Gao and Q. Wang, A consistent description of kinetic equation with triangle anomaly, Phys. Rev. D 83 (2011) 094017 [arXiv:1008.2418] [INSPIRE].
J.-W. Chen, S. Pu, Q. Wang and X.-N. Wang, Berry curvature and four-dimensional monopoles in the relativistic chiral kinetic equation, Phys. Rev. Lett. 110 (2013) 262301 [arXiv:1210.8312] [INSPIRE].
Y. Hidaka, S. Pu and D.-L. Yang, Relativistic chiral kinetic theory from quantum field theories, Phys. Rev. D 95 (2017) 091901 [arXiv:1612.04630] [INSPIRE].
C. Manuel and J. M. Torres-Rincon, Kinetic theory of chiral relativistic plasmas and energy density of their gauge collective excitations, Phys. Rev. D 89 (2014) 096002 [arXiv:1312.1158] [INSPIRE].
C. Manuel and J. M. Torres-Rincon, Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory, Phys. Rev. D 90 (2014) 076007 [arXiv:1404.6409] [INSPIRE].
Y. Wu, D. Hou and H.-C. Ren, Field theoretic perspectives of the Wigner function formulation of the chiral magnetic effect, Phys. Rev. D 96 (2017) 096015 [arXiv:1601.06520] [INSPIRE].
N. Mueller and R. Venugopalan, Worldline construction of a covariant chiral kinetic theory, Phys. Rev. D 96 (2017) 016023 [arXiv:1702.01233] [INSPIRE].
N. Mueller and R. Venugopalan, The chiral anomaly, Berry’s phase and chiral kinetic theory, from world-lines in quantum field theory, Phys. Rev. D 97 (2018) 051901 [arXiv:1701.03331] [INSPIRE].
A. Huang, S. Shi, Y. Jiang, J. Liao and P. Zhuang, Complete and consistent chiral transport from Wigner function formalism, Phys. Rev. D 98 (2018) 036010 [arXiv:1801.03640] [INSPIRE].
J.-H. Gao, Z.-T. Liang, Q. Wang and X.-N. Wang, Disentangling covariant Wigner functions for chiral fermions, Phys. Rev. D 98 (2018) 036019 [arXiv:1802.06216] [INSPIRE].
S. Carignano, C. Manuel and J. M. Torres-Rincon, Consistent relativistic chiral kinetic theory: a derivation from on-shell effective field theory, Phys. Rev. D 98 (2018) 076005 [arXiv:1806.01684] [INSPIRE].
S. Lin and A. Shukla, Chiral kinetic theory from effective field theory revisited, JHEP 06 (2019) 060 [arXiv:1901.01528] [INSPIRE].
S. Carignano, C. Manuel and J. M. Torres-Rincon, Chiral kinetic theory from the on-shell effective field theory: derivation of collision terms, Phys. Rev. D 102 (2020) 016003 [arXiv:1908.00561] [INSPIRE].
Y.-C. Liu, L.-L. Gao, K. Mameda and X.-G. Huang, Chiral kinetic theory in curved spacetime, Phys. Rev. D 99 (2019) 085014 [arXiv:1812.10127] [INSPIRE].
N. Weickgenannt, X.-L. Sheng, E. Speranza, Q. Wang and D. H. Rischke, Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism, Phys. Rev. D 100 (2019) 056018 [arXiv:1902.06513] [INSPIRE].
J.-H. Gao and Z.-T. Liang, Relativistic quantum kinetic theory for massive fermions and spin effects, Phys. Rev. D 100 (2019) 056021 [arXiv:1902.06510] [INSPIRE].
K. Hattori, Y. Hidaka and D.-L. Yang, Axial kinetic theory and spin transport for fermions with arbitrary mass, Phys. Rev. D 100 (2019) 096011 [arXiv:1903.01653] [INSPIRE].
Z. Wang, X. Guo, S. Shi and P. Zhuang, Mass correction to chiral kinetic equations, Phys. Rev. D 100 (2019) 014015 [arXiv:1903.03461] [INSPIRE].
D.-L. Yang, K. Hattori and Y. Hidaka, Effective quantum kinetic theory for spin transport of fermions with collsional effects, JHEP 07 (2020) 070 [arXiv:2002.02612] [INSPIRE].
Y.-C. Liu, K. Mameda and X.-G. Huang, Covariant spin kinetic theory I: collisionless limit, Chin. Phys. C 44 (2020) 094101 [arXiv:2002.03753] [INSPIRE].
T. Hayata, Y. Hidaka and K. Mameda, Second order chiral kinetic theory under gravity and antiparallel charge-energy flow, JHEP 05 (2021) 023 [arXiv:2012.12494] [INSPIRE].
S. Chen, Z. Wang and P. Zhuang, Equal-time kinetic equations in a rotational field, arXiv:2101.07596 [INSPIRE].
D. Vasak, M. Gyulassy and H. T. Elze, Quantum transport theory for Abelian plasmas, Annals Phys. 173 (1987) 462 [INSPIRE].
H. T. Elze, M. Gyulassy and D. Vasak, Transport equations for the QCD quark Wigner operator, Nucl. Phys. B 276 (1986) 706 [INSPIRE].
H.-T. Elze and U. W. Heinz, Quark-gluon transport theory, Phys. Rept. 183 (1989) 81 [INSPIRE].
P. Zhuang and U. W. Heinz, Relativistic quantum transport theory for electrodynamics, Annals Phys. 245 (1996) 311 [nucl-th/9502034] [INSPIRE].
X.-L. Sheng, Wigner function for spin-1/2 fermions in electromagnetic fields, Ph.D. thesis, Frankfurt U., Frankfurt, Germany (2019) [arXiv:1912.01169] [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].
J.-H. Gao, J.-Y. Pang and Q. Wang, Chiral vortical effect in Wigner function approach, Phys. Rev. D 100 (2019) 016008 [arXiv:1810.02028] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
S.-Z. Yang, J.-H. Gao, Z.-T. Liang and Q. Wang, Second-order charge currents and stress tensor in a chiral system, Phys. Rev. D 102 (2020) 116024 [arXiv:2003.04517] [INSPIRE].
N. Weickgenannt, E. Speranza, X.-L. Sheng, Q. Wang and D. H. Rischke, Generating spin polarization from vorticity through nonlocal collisions, arXiv:2005.01506 [INSPIRE].
Z. Wang, X. Guo and P. Zhuang, Local equilibrium spin distribution from detailed balance, arXiv:2009.10930 [INSPIRE].
N. Weickgenannt, E. Speranza, X.-L. Sheng, Q. Wang and D. H. Rischke, Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory, arXiv:2103.04896 [INSPIRE].
X.-L. Sheng, N. Weickgenannt, E. Speranza, D. H. Rischke and Q. Wang, From Kadanoff-Baym to Boltzmann equations for massive spin-1/2 fermions, arXiv:2103.10636 [INSPIRE].
D. Hou and S. Lin, Polarization rotation of chiral fermions in vortical fluid, Phys. Lett. B 818 (2021) 136386 [arXiv:2008.03862] [INSPIRE].
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Lin, S., Yang, L. Magneto-vortical effect in strong magnetic field. J. High Energ. Phys. 2021, 54 (2021). https://doi.org/10.1007/JHEP06(2021)054
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DOI: https://doi.org/10.1007/JHEP06(2021)054