  We argue that the strongly coupled quark-gluon plasma formed at LHC and RHIC
can be considered as a chiral superfluid. The "normal" component of the fluid
is the thermalized matter in common sense, while the "superfluid" part consists
of long wavelength (chiral) fermionic states moving independently. We use the
bosonization procedure with a finite cut-off and obtain a dynamical axion-like
field out of the chiral fermionic modes. Then we use relativistic hydrodynamics
for macroscopic description of the effective theory obtained after the
bosonization. Finally, solving the hydrodynamic equations in gradient
expansion, we find that in the presence of external electromagnetic fields or
rotation the motion of the "superfluid" component gives rise to the chiral
magnetic, chiral vortical, chiral electric and dipole wave effects. Latter two
effects are specific for a two-component fluid, which provides us with crucial
experimental tests of the model.
