  We outline a novel chiral kinetic theory framework for systematic
computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion
collisions. The real part of the fermion determinant in the QCD effective
action is expressed as a supersymmetric world-line action of spinning, colored,
Grassmanian point particles in background gauge fields, with equations of
motion that are covariant generalizations of the Bargmann-Michel-Telegdi and
Wong equations. Berry's phase is obtained in a consistent non-relativistic
adiabatic limit. The chiral anomaly, in contrast, arises from the phase of the
fermion determinant; its topological properties are therefore distinct from
those of the Berry phase. We show that the imaginary contribution to the
fermion determinant too can be expressed as a point particle world-line path
integral and derive the corresponding anomalous axial vector current. Our
results can be used to derive a covariant relativistic chiral kinetic theory
including the effects of topological fluctuations that has overlap with
classical-statistical simulations of the CME at early times and anomalous
hydrodynamics at late times.
