The chiral magnetic effect and the chiral spin symmetry in QCD above Tc

Abstract: The chiral magnetic effect (CME) is an exact statement that connects via the axial anomaly the electric current in a system consisting of interacting fermions and gauge field with chirality imbalance that is put into a strong external magnetic field. Experimental search of the magnetically induced current in QCD in heavy ion collisions above a pseudocritical temperature hints, though not yet conclusive, that the induced current is either small or vanishing. This would imply that the chirality imbalance in QCD above $T_c$ that could be generated via topological fluctuations is at most very small. Here we present the most general reason for absence (smallness) of the chirality imbalance in QCD above Tc. It was recently found on the lattice that QCD above Tc is approximately chiral spin (CS) symmetric with the symmetry breaking at the level of a few percent. The CS transformations mix the right- and left-handed components of quarks. Then an exact CS symmetry would require absence of any chirality imbalance. Consequently an approximate CS symmetry admits at most a very small chirality imbalance in QCD above Tc. Hence the absence or smallness of an magnetically induced current observed in heavy ion collisions could be considered as experimental evidence for emergence of the CS symmetry above Tc.