At the level of hadrons, pseudoscalar mesons, the ambit of the chiral model, the chiral SU ( 2 ) L × × SU ( 2 ) R group is spontaneously broken down to SU ( 2 ) V , by the QCD vacuum. That is, it is realized nonlinearly, in the Nambu–Goldstone mode : The Q V annihilate the vacuum, but the Q A do not! This is visualized nicely through a geometrical argument based on the fact that the Lie algebra of SU ( 2 ) L × × SU ( 2 ) R is isomorphic to that of SO(4). The unbroken subgroup, realized in the linear Wigner–Weyl mode, is SO ( 3 ) ⊂ ⊂ SO ( 4 ) which is locally isomorphic to SU(2) (V: isospin).