  We prove Abelian magnetic monopole dominance in the string tension of QCD.
Abelian and monopole dominance in low energy physics of QCD has been confirmed
for various quantities by recent Monte Carlo simulations of lattice gauge
theory. In order to prove this dominance, we use the reformulation of continuum
Yang-Mills theory in the maximal Abelian gauge as a deformation of a
topological field theory of magnetic monopoles, which was proposed in the
previous article by the author. This reformulation provides an efficient way
for incorporating the magnetic monopole configuration as a topological
non-trivial configuration in the functional integral. We derive a version of
the non-Abelian Stokes theorem and use it to estimate the expectation value of
the Wilson loop. This clearly exhibits the role played by the magnetic monopole
as an origin of the Berry phase in the calculation of the Wilson loop in the
manifestly gauge invariant manner. We show that the string tension derived from
the diagonal (abelian) Wilson loop in the topological field theory (studied in
the previous article) converges to that of the full non-Abelian Wilson loop in
the limit of large Wilson loop. Therefore, within the above reformulation of
QCD, this result (together with the previous result) completes the proof of
quark confinement in QCD based on the criterion of the area law of the full
non-Abelian Wilson loop.
