= Chiral symmetry
{title2=$SU(2)_L\times SU(2)_R$}
<Chiral symmetry> allows independent flavor rotations of left-handed and right-handed fields. For two massless quark flavors, the non-Abelian chiral transformations form $SU(2)_L\times SU(2)_R$. The additional vector $U(1)$ symmetry of <baryon number> acts trivially on the <pion> field $U$. The low-energy <pion> field $U\in SU(2)$ transforms as $U\mapsto LUR^\dagger$. Its derivative <Skyrme model> terms are invariant under constant $L,R$. A chosen vacuum $U=1$ preserves the diagonal subgroup $L=R$, which acts by conjugation and is the <isospin> symmetry. An ordinary common nonzero <pion> mass explicitly breaks the independent left/right symmetry to that vector subgroup; vacuum selection in the massless theory is instead <spontaneous symmetry breaking>. The singlet axial anomaly is a separate issue and is not part of this two-flavor non-anomalous group.
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