  Some time ago, Atiyah showed that there exists a natural identification
between the k-instantons of a Yang-Mills theory with gauge group $G$ and the
holomorphic maps from $CP_1$ to $\Omega G$. Since then, Nair and Mazur, have
associated the $\Theta $ vacua structure in QCD with self-intersecting Riemann
surfaces immersed in four dimensions. From here they concluded that these 2D
surfaces correspond to the non-perturbative phase of QCD and carry the
topological information of the $\Theta$ vacua. In this paper we would like to
elaborate on this point by making use of Atiyah's identification. We will argue
that an effective description of QCD may be more like a $WZW$ model coupled to
the induced metric of an immersion of a 2-D Riemann surface in $R^4$. We make
some further comments on the relationship between the coadjoint orbits of the
Kac-Moody group on $G$ and instantons with axial symmetry and monopole charge.
