Abstract
We present a real-time lattice approach to study the non-equilibrium dynamics of vector and axial charges in $SU(N) \times U(1)$ gauge theories. Based on a classical description of the non-Abelian and Abelian gauge fields, we include dynamical fermions and develop operator definitions for (improved) Wilson and overlap fermions that allow us to study real-time manifestations of the axial anomaly from first principles. We present a first application of this approach to anomalous transport phenomena such as the Chiral Magnetic Effect (CME) and Chiral Separation Effect (CSE) by studying the dynamics of fermions during and after a $SU(N)$ sphaleron transition in the presence of a $U(1)$ magnetic field. We investigate the fermion mass and magnetic field dependence of the suggested signatures of the CME and CSE and point out some important aspects which need to be accounted for in the macroscopic description of anomalous transport phenomena.
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