  We discuss within the weak-field approximation and the derivative expansion
how the area law of the Wilson loop follows directly from the vacuum condensate
of mass dimension 2, i.e., simultaneous Bose-Einstein condensation of gluon
pair and ghost-antighost pair. Such a novel vacuum condensate was recently
claimed to exist as the non-vanishing vacuum expectation value of a
BRST-invariant composite operator of mass dimension 2. First of all, we use a
version of the non-Abelian Stokes theorem to rewrite the Wilson loop line
integral to a surface integral. Then we convert the Yang-Mills theory with an
insertion of the Wilson loop operator into a bosonic string theory with a
rigidity term by way of an equivalent antisymmetric tensor gauge theory which
couples to the surface spanned by the Wilson loop. This result suggests an
intimate relationship between quark confinement and mass gap in Yang-Mills
theory. In fact, the dual Ginzburg-Landau theory describing the dual
superconductivity is also derivable by making use of duality transformations
without using the naive Abelian projection and without breaking the global
color invariance of the original Yang-Mills theory. This feature is desirable
from the viewpoint of color confinement preserving color symmetry.
