Editing Quantum chromodynamics (section)

===Symmetry groups===
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 [[Quantum electrodynamics|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 ([[chirality (physics)|chiral]]) flavor symmetry group SU<sub>L</sub>(''N<sub>f</sub>'') &times; SU<sub>R</sub>(''N<sub>f</sub>'') &times; U<sub>B</sub>(1) &times; U<sub>A</sub>(1). The chiral symmetry is [[spontaneous symmetry breaking|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 (physics)|anomaly]]. Gluon field configurations called [[instanton]]s are closely related to this anomaly.

There are two different types of SU(3) symmetry: there is the symmetry that acts on the different colors of quarks, and this is an exact gauge symmetry mediated by the gluons, and there is also a flavor symmetry that rotates different flavors of quarks to each other, or ''flavor SU(3)''. Flavor SU(3) is an approximate symmetry of the vacuum of QCD, and is not a fundamental symmetry at all. It is an accidental consequence of the small mass of the three lightest quarks.

In the [[QCD vacuum]] there are vacuum condensates of all the quarks whose mass is less than the QCD scale. This includes the up and down quarks, and to a lesser extent the strange quark, but not any of the others. The vacuum is symmetric under SU(2) [[isospin]] rotations of up and down, and to a lesser extent under rotations of up, down, and strange, or full flavor group SU(3), and the observed particles make isospin and SU(3) multiplets.

The approximate flavor symmetries do have associated gauge bosons, observed particles like the rho and the omega, but these particles are nothing like the gluons and they are not massless. They are emergent gauge bosons in an approximate [[AdS/QCD|string description of QCD]].