SU(2N_F) hidden symmetry of QCD

Abstract

Recently a global SU(4) \supset SU(2)_L \times SU(2)_R \times U(1)_A symmetry of the confining Coulombic part of the QCD Hamiltonian has been discovered with N_F=2. This global symmetry includes both independent rotations of the left- and right-handed quarks in the isospin space as well as the chiralspin rotations that mix the left- and right-handed components of the quark fields. It has been suggested by lattice simulations, however, that a symmetry of mesons in the light quark sector upon the quasi-zero mode truncation from the quark propagators is actually higher than SU(4), because the states from a singlet and a 15-plet irreducible representations of SU(4) are also degenerate. Here we demonstrate that classically QCD, ignoring irrelevant exact zero mode contributions, has a SU(2N_F) symmetry. If effects of dynamical chiral symmetry breaking and of anomaly are encoded in the same near-zero modes, then truncation of these modes should restore a classical SU(2N_F) symmetry. Then we show in a Lorentz- and gauge-invariant manner emergence of a bilocal SU(4) \times SU(4) symmetry in mesons that contains a global SU(4) as a subgroup upon truncation of the quasi-zero modes. We also demonstrate that the confining Coulombic part of the QCD Hamiltonian has this bilocal symmetry. It explains naturally a degeneracy of different irreducible representations of SU(4) observed in lattice simulations.