The Abelian projection versus the Hitchin fibration of K(D) pairs in four-dimensional QCD

We point out that the concept of Abelian projection gives us a physical interpretation of the role that the Hitchin fibration of parabolic K(D) pairs plays in the large-N limit of four-dimensional QCD. This physical interpretation furnishes also a simple criterium for the confinement of electric fluxes in the large-N limit of QCD. There is also an alternative, compatible interpretation, based on the QCD string.