Helicity conservation in perfect electromagnetic and chiral fluids

Abstract

We derive the total helicity conservation law for a perfect electromagnetic relativistic fluid. As the conservation equation contains the derivative of the magnetic helicity, it can be reshaped as having the same form as the chiral anomaly equation if the fluid is isentropic. We also take the non-relativistic limit of the helicity conservation law, and check the agreement with the Abanov-Wiegmann equation at zero temperature, but we provide further corrections in the more general case. We then consider chiral fluids, when the chiral anomaly equation has to be incorporated in the hydrodynamical equations, together with other chiral transport effects which exist in the presence of a chiral imbalance. We finally study how the chiral imbalance modifies the helicity conservation law.

v2: 17 pages, with additional explanations and an updated reference list. Version to be published in Phys.Rev.D journal

References in corpus (7)

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• The chiral magnetic effect in hydrodynamical approach
• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
• Experimental searches for the chiral magnetic effect in heavy-ion collisions
• An introduction to relativistic hydrodynamics
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