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We outline a novel chiral kinetic theory framework for systematiccomputations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ioncollisions. The real part of the fermion determinant in the QCD effectiveaction is expressed as a supersymmetric world-line action of spinning, colored,Grassmanian point particles in background gauge fields, with equations ofmotion that are covariant generalizations of the Bargmann-Michel-Telegdi andWong equations. Berry's phase is obtained in a consistent non-relativisticadiabatic limit. The chiral anomaly, in contrast, arises from the phase of thefermion determinant; its topological properties are therefore distinct fromthose of the Berry phase. We show that the imaginary contribution to thefermion determinant too can be expressed as a point particle world-line pathintegral and derive the corresponding anomalous axial vector current. Ourresults can be used to derive a covariant relativistic chiral kinetic theoryincluding the effects of topological fluctuations that has overlap withclassical-statistical simulations of the CME at early times and anomaloushydrodynamics at late times.

The chiral anomaly, Berry's phase and chiral kinetic theory, from world-lines in quantum field theory