Abstract
The response of chiral fermions to time and space dependent axial imbalance & constant magnetic field is analyzed. The axialvector-vector-vector (AVV) three-point function is studied using a real-time approach at finite temperature in the weak external field approximation. The chiral magnetic conductivity is given analytically for noninteracting fermions. It is pointed out that local charge conservation plays an important role when the axial imbalance is inhomogeneous. Proper regularization is needed which makes the constant axial imbalance limit delicate: for static but spatially oscillating chiral charge the current of the chiral magnetic effect (CME) vanishes. In the homogeneous (but possible time-dependent) limit of the axial imbalance the CME current is determined solely by the chiral anomaly. As a phenomenological consequence, the observability of the charge asymmetry caused by the CME turns out to be a matter of interplay between various scales of the system. Possible plasma instabilities resulting from the gradient corrections to the CME current are also pointed out.
Highlights
Induced transport phenomena in systems with chiral fermions have attracted wide interests ranging from high energy physics to condensed matter physics
The previous statement on the vanishing of the long-time transported charge ΔQ is generalized beyond the weak-coupling approximation: it is a consequence of the Ward-identity, i.e., local charge conservation, which is valid in all orders of the perturbation theory
In weakly coupled QED we derived the explicit form of the real-time response function in Eq (31), which interpolates between the anomaly ruled chiral magnetic effect (CME) current like in
Summary
Induced transport phenomena in systems with chiral fermions have attracted wide interests ranging from high energy physics to condensed matter physics. The predictions of CME include the electric charge asymmetries in the final stage of the relativistic heavy ion collisions (RHIC) [3,4,5,6] and the negative magnetoresistance in some Weyl and Dirac semimetals [7,8,9,10,11,12]. In the former case, a strong magnetic field is generated during an off-central collision and the chirality imbalance is induced by the transition among different topological sectors.
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