  We derive an effective action for charged plasmas with an anomalous (abelian)
global current charge current using holography. The holographic description is
captured by the dynamics of an Einstein-Maxwell-Chern-Simons theory in an
asymptotically AdS spacetime. The 't Hooft anomaly contribution, which is
encoded in the Chern-Simons term, contributes at the Gaussian order in the
effective action only in the momentum diffusion sector, where it leads to
chiral shear waves. However, as we demonstrate, beyond the Gaussian order,
there is a non-trivial imprint of the parity-violating anomaly term in sound
and charge diffusion dynamics as well.
