Page "Quantum chromodynamics" Paragraph 29

The color group SU ( 3 ) corresponds to the local symmetry whose gauging gives rise to QCD.

The electric charge labels a representation of the local symmetry group U ( 1 ) which is gauged to give QED: this is an abelian group.

If one considers a version of QCD with N < sub > f </ sub > flavors of massless quarks, then there is a global ( chiral ) flavor symmetry group SU < sub > L </ sub >( N < sub > f </ sub >) × SU < sub > R </ sub >( N < sub > f </ sub >) × U < sub > B </ sub >( 1 ) × U < sub > A </ sub >( 1 ).

The chiral symmetry is spontaneously broken by the QCD vacuum to the vector ( L + R ) SU < sub > V </ sub >( N < sub > f </ sub >) with the formation of a chiral condensate.

The vector symmetry, U < sub > B </ sub >( 1 ) corresponds to the baryon number of quarks and is an exact symmetry.

The axial symmetry U < sub > A </ sub >( 1 ) is exact in the classical theory, but broken in the quantum theory, an occurrence called an anomaly.

Gluon field configurations called instantons are closely related to this anomaly.