  By means of a certain exact non-abelian duality transformation, we show that
there is a natural embedding, dense in the sense of the distributions in the
large-N limit, of parabolic Higgs bundles of rank N on a fiber two-dimensional
torus into the QCD functional integral, fiberwise over the base two-dimensional
torus of the trivial elliptic fibration on which the four-dimensional theory is
defined. The moduli space of parabolic Higgs bundles of rank N is an integrable
Hamiltonian system, that admits a foliation by the moduli of holomorphic line
bundles over N-sheeted spectral covers (or, what is the same, over a space of N
gauge-invariant polynomials), the Hitchin fibration. According to Hitchin, the
Higgs bundles can be recovered from the spectral covers and the line bundles.
If the N invariant polynomials together with the abelian connection on the line
bundles are chosen as the N+1 collective fields of the Hitchin fibration, all
the entropy of the functional integration over the moduli of the Higgs bundles
is absorbed, in the large-N limit, into the Jacobian determinant of the change
of variables to the collective fields of the Hitchin fibration. Hence, the
large-N limit is dominated by the saddle-point of the effective action as in
vector-like models.
