  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.
