Recent evidence from relativistic heavy ion collisions (HIC) experiments  confirmed the global significance of the vorticity to polarisation transfer through the spin-orbit coupling predicted by the Dirac equation. This transfer can be related to anomalous transport phenomena, which are believed to originate from the breaking of classical symmetries via the so-called quantum anomalies (e.g., the  axial anomaly). Aside from the well-known vector (gauge) and chiral (axial) symmetries that have been extensively used to study anomalous transport, this talk discusses the impact of the symmetry of the Dirac Lagrangian with respect to helicity transformations. This symmetry gives rise to the helicity charge current, which has the advantage of being classically conserved for any fermion mass.

By considering a thermal bath under rigid rotation, the vector, axial and helical chemical potentials are shown to form a triad, giving rise to the axial-helical-vortical effects. The emergence of the helicity chemical potential as a thermodynamic degree of freedom is shown to open the door to the helical vortical waves, representing a new type of gapless excitations that can propagate in fermionic matter under rotation. Furthermore, the laws governing the helical vortical transport are shown to remain robust for masses up to the thermal energy, under HIC conditions. Finally,the helical and vector chemical potentials are shown to play a symmetric role at the level of the QCD phase diagram in the context of the linear sigma model with quarks, while a finite axial chemical potential is excluded within this theory.

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