On the absence of the Chiral Magnetic Effect in equilibrium QCD

In this paper we investigate the chiral magnetic effect (CME): the generation of an electric current due to a homogeneous background magnetic field and a homogeneous chiral imbalance in QCD. We demonstrate that the leading coefficient describing the CME vanishes in equilibrium, both for free fermions as well as in full QCD. Our full QCD results are based on continuum extrapolated lattice simulations using dynamical staggered quarks with physical masses as well as quenched Wilson quarks. We show that it is crucial that a gauge invariant ultraviolet regularization is used to compute the CME and elaborate on why some of the existing in-equilibrium calculations of this effect gave a nonzero result. We stress that our findings imply the absence of a time-independent CME current flowing in equilibrium QCD, but do not concern the CME as an out-of-equilibrium, time-dependent effect.