Abstract
Gauge theories with compact symmetry groups possess topologically non-trivial configurations of gauge field. This has dramatic implications for the vacuum structure of Quantum Chromo-Dynamics (QCD) and for the behavior of QCD plasma, as well as for condensed matter systems with chiral quasiparticles. I review the current status of the problem with an emphasis on the interplay of chirality with a background magnetic field, and on the observable manifestations of topology in heavy ion collisions, Dirac semimetals, neutron stars, and in the Early Universe.
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