Abstract
We show that barotropic flows of a perfect, charged, classical fluid exhibit an anomaly analogous to the chiral anomaly known in quantum field theories with Dirac fermions. A prominent effect of the chiral anomaly is the transport electric current in the fluid at equilibrium with the chiral reservoir. We find that it is also a property of celebrated Beltrami flows — stationary solutions of the Euler equation with an extensive helicity.
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D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Effective actions for anomalous hydrodynamics, JHEP 03 (2014) 034 [arXiv:1312.0610] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Anomaly inflow and thermal equilibrium, JHEP 05 (2014) 134 [arXiv:1310.7024] [INSPIRE].
A.G. Abanov and P.B. Wiegmann, Axial-current anomaly in Euler fluids, Phys. Rev. Lett. 128 (2022) 054501 [arXiv:2110.11480] [INSPIRE].
T.D.C. Bevan et al., Momentum creation by vortices in superfluid 3He as a model of primordial baryogenesis, Nature 386 (1997) 689.
M.M. Salomaa and G.E. Volovik, Quantized vortices in superfluid 3He, Rev. Mod. Phys. 59 (1987) 533 [Erratum ibid. 60 (1988) 573] [INSPIRE].
A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].
D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The effects of topological charge change in heavy ion collisions: ‘event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [INSPIRE].
A.Y. Alekseev, V.V. Cheianov and J. Fröhlich, Universality of transport properties in equilibrium, Goldstone theorem and chiral anomaly, Phys. Rev. Lett. 81 (1998) 3503 [cond-mat/9803346] [INSPIRE].
J. Fröhlich and B. Pedrini, New applications of the chiral anomaly, in Mathematical physics 2000, World Scientific, Singapore (2000), p. 9.
R. Landauer, Electrical resistance of disordered one-dimensional lattices, Phil. Mag. 21 (1970) 863.
M. Büttiker, Four-terminal phase-coherent conductance, Phys. Rev. Lett. 57 (1986) 1761.
M.N. Chernodub, Y. Ferreiros, A.G. Grushin, K. Landsteiner and M.A.H. Vozmediano, Thermal transport, geometry, and anomalies, arXiv:2110.05471 [INSPIRE].
I. Rogachevskii et al., Laminar and turbulent dynamos in chiral magnetohydrodynamics. I. Theory, Astrophys. J. 846 (2017) 153 [arXiv:1705.00378] [INSPIRE].
A. Avdoshkin, V.P. Kirilin, A.V. Sadofyev and V.I. Zakharov, On consistency of hydrodynamic approximation for chiral media, Phys. Lett. B 755 (2016) 1 [arXiv:1402.3587] [INSPIRE].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
J.S. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].
S. Treiman and R. Jackiw, Current algebra and anomalies, Princeton University Press, Princeton, NJ, U.S.A. (1986).
H.K. Moffatt, The degree of knottedness of tangled vortex lines, J. Fluid Mech. 35 (1969) 117.
V.E. Zakharov and E.A. Kuznetsov, Hamiltonian formalism for nonlinear waves, Phys. Usp. 40 (1997) 1087.
V.I. Arnold and B.A. Khesin, Topological methods in hydrodynamics, Springer, New York, NY, U.S.A. (1998).
J.D. Bekenstein, Helicity conservation laws for fluids and plasmas, Astrophys. J. 319 (1987) 207.
B. Khesin and Y. Chekanov, Invariants of the Euler equations for ideal or barotropic hydrodynamics and superconductivity in D dimensions, Physica D 40 (1989) 119.
B. Grossman, Does a dyon leak?, Phys. Rev. Lett. 50 (1983) 464 [INSPIRE].
L.D. Faddeev, Operator anomaly for the Gauss law, Phys. Lett. B 145 (1984) 81 [INSPIRE].
B. Carter, Perfect fluid and magnetic field conservation laws in the theory of black hole accretion rings, in Active galactic nuclei, Cambridge University Press, Cambridge, U.K. (1979), p. 273.
A. Lichnerowicz, Relativistic hydrodynamics, in Magnetohydrodynamics: waves and shock waves in curved space-time, Springer, Dordrecht, The Netherlands (1994), p. 98.
E. Gourgoulhon, An introduction to relativistic hydrodynamics, EAS Publ. Ser. 21 (2006) 43.
D.G. Dritschel, Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics, J. Fluid Mech. 222 (1991) 525.
A. Morgulis, V.I. Yudovich and G.M. Zaslavsky, Compressible helical flows, Commun. Pure Appl. Math. 48 (1995) 571.
A. Enciso and D. Peralta-Salas, Beltrami fields with a nonconstant proportionality factor are rare, Arch. Ration. Mech. Anal. 220 (2015) 243.
D.E. Kharzeev and D.T. Son, Testing the chiral magnetic and chiral vortical effects in heavy ion collisions, Phys. Rev. Lett. 106 (2011) 062301 [arXiv:1010.0038] [INSPIRE].
G.M. Monteiro, A.G. Abanov and V.P. Nair, Hydrodynamics with gauge anomaly: variational principle and Hamiltonian formulation, Phys. Rev. D 91 (2015) 125033 [arXiv:1410.4833] [INSPIRE].
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Wiegmann, P.B., Abanov, A.G. Chiral anomaly in Euler fluid and Beltrami flow. J. High Energ. Phys. 2022, 38 (2022). https://doi.org/10.1007/JHEP06(2022)038
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DOI: https://doi.org/10.1007/JHEP06(2022)038