Bag Formation from Gauge Condensate

TL;DR

This paper proposes a gauge condensate model with a four-index field strength that describes both confinement and perturbative phases, naturally deriving MIT bag boundary conditions through phase matching.

Contribution

It introduces a novel effective action involving a four-index field strength to unify confinement and perturbative phases in QCD, respecting Poincare invariance.

Findings

The model describes both confinement and perturbative phases.

Phase transition is mediated by membranes with MIT bag boundary conditions.

The four-index field strength does not add degrees of freedom in the unconfined phase.

Abstract

As it is well known, one can lower the energy of the trivial perturbation QCD vacuum by introducing a non-vanishing chromomagnetic field strength. This happens because radiative corrections produce an effective action of the form $f(F_{\mu\nu}^aF^{\mu\nu a})$ with $f'(y_0)=0$ for some $y_0\neq 0$. However, a vacuum with a non zero field strength is not consistent with Poincare Invariance (PI). Generalizing this type of effective action by introducing, in the simplest way, a four index field strength $\partial_{[\mu}A_{\nu\alpha\beta]}$, 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 4-index field strength does not introduce new degrees of freedom, while in the confined phase both 4-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 3-index potentials from which the 4-index field strength derive, leads automatically to the MIT bag boundary conditions for the gauge fields living inside the bubble containing the perturbative phase.