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Abstract
We modify a kinetic theory of massless fermions to incorporate the effects of the conformal anomaly. Working in a collisionless regime, we emulate the conformal anomaly via a momentum-dependent electric coupling. In this prescription, the conformal anomaly leads to a hedgehog-like structure in the momentum space similar to the Berry phase associated with the axial anomaly. The interplay between the axial and conformal anomalies generates the axial current, proportional to the helicity flow of the electromagnetic background. The corresponding conductivity is determined by the running of the electric coupling between the tip of the Dirac cone and the Fermi surface.
Highlights
Chiral fermions appear in different physical environments ranging from quark-gluon plasma created in heavyion collisions [1,2] to the electronic excitations in Weyl semimetals in the solid-state physics [3,4,5]
In the vacuum of massless QED, the conformal anomaly associated with the electric coupling reveals itself in the form of anomalous transport phenomena, the scale electromagnetic effects, that are realized in the background of gravitational and electromagnetic fields [12]
The axial anomaly is known to lead to the dissipationless transport phenomena known as the chiral magnetic and chiral separation effects that generate, respectively, vector and axial currents of fermions along the axis of the background of the magnetic field (37)
Summary
Chiral fermions appear in different physical environments ranging from quark-gluon plasma created in heavyion collisions [1,2] to the electronic excitations in Weyl semimetals in the solid-state physics [3,4,5] Major properties of these systems carry an imprint of the chiral invariance respected by the classical theory of the massless spin-half particles. The chiral kinetic equation incorporating the axial anomaly into the classical kinetic theory of Weyl fermions was proposed in Refs. We make an attempt to incorporate the conformal anomaly at the level of the classical kinetic theory of massless fermions. Our last section is devoted to the conclusions where we discuss the limitations of our approach and realization of the proposed transport effects in physical systems
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