Abstract
We present a novel perspective to characterize the chiral magnetic and related effects in terms of angular decomposed modes. We find that the vector current and the chirality density are connected through a surprisingly simple relation for all the modes and any mass, which defines the mode decomposed chiral magnetic effect in such a way free from the chiral chemical potential. The mode decomposed formulation is useful also to investigate properties of rotating fermions. For demonstration, we give an intuitive account for a nonzero density emerging from a combination of rotation and magnetic field as well as an approach to the chiral vortical effect at finite density.
Highlights
Chiral fermions exhibit fascinating transport properties, the origin of which is traced back to the quantum anomaly associated with chiral symmetry
We found a remarkable relation between the vector current mode jznð;l↑;k;↓Þ and the chirality density ρð5↑n;;↓l;Þk
We would emphasize noteworthy advantages of the mode decomposed chiral magnetic effect (CME) as follows: first of all, not the chiral chemical potential but the chirality density is directly associated with the vector current
Summary
Chiral fermions exhibit fascinating transport properties, the origin of which is traced back to the quantum anomaly associated with chiral symmetry. The CME generates a vector current j in parallel to an external magnetic field B in the presence of a finite chirality imbalance. Our calculations will lead to a surprisingly simple relation between the vector current and the chirality density, which had been unseen until we made a mode decomposed formulation Both strong magnetic field B and large vorticity ω are highly relevant to the heavy-ion collisions The equation holds for the lowest landau levels (LLLs) and higher Landau levels for any mass, while a similar equation between the axial-vector current j5 and the density ρ is valid for the LLLs only The existence of such an elegant relation reminds us of the fact that the CME is anomaly protected.
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