  Starting from SU(2) Yang-Mills theory in 3+1 dimensions, we prove that the
abelian-projected effective gauge theories are written in terms of the maximal
abelian gauge field and the dual abelian gauge field interacting with monopole
current. This is performed by integrating out all the remaining non-Abelian
gauge field belonging to SU(2)/U(1). We show that the resulting abelian gauge
theory recovers exactly the same one-loop beta function as the original
Yang-Mills theory. Moreover, the dual abelian gauge field becomes massive if
the monopole condensation occurs. This result supports the dual superconductor
scenario for quark confinement in QCD. We give a criterion of dual
superconductivity and point out that the monopole condensation can be estimated
from the classical instanton configuration. Therefore there can exist the
effective abelian gauge theory which shows both asymptotic freedom and quark
confinement based on the dual Meissner mechanism. Inclusion of arbitrary number
of fermion flavors is straightforward in this approach. Some implications to
lower dimensional case will also be discussed.
