Bag formation from gauge condensate

As it is well known, one can lower the energy of the trivial perturbation QCD vacuum by introducing a nonvanishing chromomagnetic field strength. This happens because radiative corrections produce an effective action of the form f(F^a _μνF^μνa) with f'(y0) = 0 for some y0 ≠ 0. However, a vacuum with a nonzero field strength is not consistent with Poincaré Invariance (PI). Generalizing this type of effective action by introducing, in the simplest way, a four-index field strength [_μA_ναβ], which can have an expectation value without violating PI, we are lead to an effective action that can describe both a confinement phase and a perturbative phase of the theory. In the unconfined phase, the four-index field strength does not introduce new degrees of freedom, while in the confined phase both four-index field strength and ordinary gauge fields are not true degrees of freedom. The matching of these phases through membranes that couple minimally to the three-index potentials from which the four-index field strength derive, leads automatically to the MIT bag boundary conditions for the gauge fields living inside the bubble containing the perturbative phase.