Massless two-flavor QCD symmetries ($SU(2{)}_L\times SU(2{)}_R\times U(1{)}_V$)

The gauge-covariant kinetic term for two massless quarks separates into left- and right-handed parts. Independent constant unitary quark flavor rotations preserve these terms, giving classical $U(2{)}_L\times U(2{)}_R$ internal symmetry in addition to local color $SU(3)$. The singlet axial $U(1{)}_A$ has a chiral anomaly, while the nonsinglet chiral symmetry and vector baryon number remain exact quantum symmetries, up to their shared discrete identifications. Equal nonzero quark masses reduce the continuous flavor symmetry to $SU(2{)}_V\times U(1{)}_V$.