Chiralspin symmetry and its implications for QCD

Abstract

In a local gauge-invariant theory with massless Dirac fermions a symmetry of the Lorentz-invariant fermion charge is larger than a symmetry of the Lagrangian as a whole. While the Dirac Lagrangian exhibits only a chiral symmetry, the fermion charge operator is invariant under a larger symmetry group, SU(2N_F), that includes chiral transformations as well as SU(2)_{CS} chiralspin transformations that mix the right- and left-handed components of fermions. Consequently a symmetry of the electric interaction, that is driven by the charge density, is larger than a symmetry of the magnetic interaction and of the kinetic term. This allows to separate in some situations electric and magnetic contributions. In particutar, in QCD the chromo-magnetic interaction contributes only to the near-zero modes of the Dirac operator, while confining chromo-electric interaction contributes to all modes. At high temperatures, above the chiral restoration crossover, QCD exhibits approximate SU(2)_{CS} and SU(2N_F) symmetries that are incompatible with free deconfined quarks. Consequently elementary objects in QCD in this regime are quarks with a definite chirality bound by the chromo-electric field, without the chromo-magnetic effects. In this regime QCD can be described as a stringy fluid.