  In this paper we argue that the strongly coupled quark-gluon plasma 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 several
nonperturbative techniques to demonstrate that. First, we analyze the fermionic
spectrum in the deconfinement phase (Tc < T < 2 Tc) using lattice (overlap)
fermions and observe a gap between near-zero modes and the bulk of the
spectrum. Second, we use the bosonization procedure with a finite cut-off and
obtain a dynamical axion-like field out of the chiral fermionic modes. Third,
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 the motion of the "superfluid" component gives rise to
the chiral magnetic, 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.
