  In QCD matter under an external magnetic field, the chiral magnetic effect
(CME) leads to the collective gapless mode called the chiral magnetic wave
(CMW). Since dynamic universality class generally depends on low-energy gapless
modes, it is nontrivial whether the CME and the resulting CMW change that of
the second-order chiral phase transition in QCD. To address this question, we
study the critical dynamics near the chiral phase transition in massless
two-flavor QCD under an external magnetic field. By performing the dynamic
renormalization-group analysis within the epsilon expansion, we find that the
presence of the CME changes the dynamic universality class to that of model A.
We also show that the transport coefficient of the CME is not renormalized by
the critical fluctuations of the order parameter.
