Charge Fluctuations from the Chiral Magnetic Effect in Nuclear Collisions

We derive a nonlocal effective Lagrangian for the chiral magnetic effect. An electric field is generated by winding number fluctuations of the nonabelian gauge field in the presence of a strong magnetic field. We estimate the magnitude of charge asymmetry fluctuations with respect to the reaction plane induced by the chiral magnetic effect in relativistic heavy ion collisions to be less than $10^{-6}$, several orders of magnitude smaller than the signal observed in the STAR experiment.