Sufficient condition for confinement of static quarks by a vortex condensation mechanism

We derive a sufficient condition for confinement of static quarks by a vortex condensation mechanism. It admits vortices that are thick at all times at the cost of constraining them to a finite volume Γ_i whose complement is not simply connected. The confining potential V(L) is estimated in terms of the change of free energy of a system enclosed in Γ_i which is induced by a change in vorticity (= singular gauge transformation applied to boundary conditions on ?Γ_i.) For Abelian gauge theories in 3 dimensions the confining Coulomb potential is reproduced as a lower bound.