  Non-Abelian gauge theories "live" in a space-time with non-trivial topology
that can be characterized by an odd-dimensional Chern-Simons form. In QCD,
Chern-Simons form is induced by the chiral anomaly and the presence of
topological solutions; it opens a possibility for the breaking of P and CP
invariances in strong interactions ("the strong CP problem"). While there is
apparently no global P and CP violation in QCD, here I argue that topological
fluctuations in hot quark-gluon matter can become directly observable in the
presence of a very intense external magnetic field by inducing local P- and CP-
odd effects. These phenomena can be described by using the Maxwell-Chern-Simons
electrodynamics as an effective theory. Local P and CP violation in hot QCD
matter can be observed in experiment through the "chiral magnetic effect" - the
separation of electric charge along the axis of magnetic field that is created
by the colliding relativistic ions. There is a recent evidence for the electric
charge separation relative to the reaction plane of heavy ion collisions from
the STAR Collaboration at RHIC.
