QCD vacuum

The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by infinitely many non-vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.

Another field-theoretic vacuum is the QED vacuum of quantum electrodynamics.

Symmetries and symmetry breaking

Symmetries of the QCD Lagrangian

Like any relativistic quantum field theory, QCD enjoys Poincaré symmetry including the discrete symmetries CPT (each of which is realized). Apart from these space-time symmetries, it also has internal symmetries. Since QCD is an SU(3) gauge theory, it has local SU(3) gauge symmetry.

Since it has many flavours of quarks, it has approximate flavour and chiral symmetry. This approximation is said to involve the chiral limit of QCD. Of these chiral symmetries, the baryon number symmetry is exact. Some of the broken symmetries include the axial U(1) symmetry of the flavour group. This is broken by the chiral anomaly. The presence of instantons implied by this anomaly also breaks CP symmetry.