  We study the anomaly induced effects of dense baryonic matter under rotation.
We derive the anomalous terms that account for the chiral vortical effect in
the low-energy effective theory for light Nambu-Goldstone modes. The anomalous
terms lead to new physical consequences, such as the anomalous Hall energy
current and spontaneous generation of angular momentum in a magnetic field (or
spontaneous magnetization by rotation). In particular, we show that, due to the
presence of such anomalous terms, the ground state of the quantum
chromodynamics (QCD) under sufficiently fast rotation becomes the "chiral
soliton lattice" of neutral pions that has lower energy than the QCD vacuum and
nuclear matter. We briefly discuss the possible realization of the chiral
soliton lattice induced by a fast rotation in noncentral heavy ion collisions.
