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, S U ( 2 N F ) , that includes chiral transformations as well as S U ( 2 ) C S chiralspin transformations that mix the right- and left-handed components of fermions. Consequently, a symmetry of the electric interaction, which is driven by the charge density, is larger than a symmetry of the magnetic interaction and of the kinetic term. This allows separating in some situations electric and magnetic contributions. In particular, 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 S U ( 2 ) C S and S U ( 2 N 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.