Testing the $SU(4)$ degeneracy after low-mode removal with $J=2$ mesons

Recent lattice results on Dirac low-mode removed $J=1,2$ mesons and $J=\frac{1}{2}$ baryons reveal the appearance of a new $SU(4)$ symmetry of confinement. Here the degeneracy of all $J=2$ iso-vector states within an irreducible representation of $SU(4)$ after low-mode removal is demonstrated. The $SU(4)$ symmetry contains $SU(2{)}_L\times SU(2{)}_R$ and $U(1{)}_A$ symmetries as subgroups and mixes all compontents $u_L,u_R,d_L,d_R$ of the two-flavor Dirac field. It implies the vanishing of the interaction of quarks with the color-magnetic field, which is shown by using the QCD Hamiltonian in Coulomb gauge.