An external Abelian magnetic field excites in the QCD vacuum a tensor supercurrent that represents the tensor polarization of the chiral condensate. This tensor supercurrent can be deduced from the chiral Lagrangian in the presence of anomalies; a similar tensor supercurrent emerges in rotating systems at finite chemical potential. We discuss the microscopic origin of this supercurrent and argue that it screens the instanton–anti-instanton molecules I I ˉ in the QCD vacuum, similarly to the vector supercurrent screening Abrikosov vortices in a superconductor. A number of possible experimental manifestations of the tensor supercurrent are discussed: (i)?spin alignment of axial-vector and vector mesons in heavy ion collisions; (ii)?tensor charge of the nucleon; (iii)?transversity of quark distributions in polarized nucleons.
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