  We prove an analogue in higher dimensions of the classical
Narasimhan-Seshadri theorem for strongly stable vector bundles of degree 0 on a
smooth projective variety $X$ with a fixed ample line bundle $\Theta$. As
applications, over fields of characteristic zero, we give a new proof of the
main theorem in a recent paper of Balaji and Koll\'ar and derive an effective
version of this theorem; over uncountable fields of positive characteristics,
if $G$ is a simple and simply connected algebraic group and the characteristic
of the field is bigger than the Coxeter index of $G$, we prove the existence of
strongly stable principal $G$ bundles on smooth projective surfaces whose
holonomy group is the whole of $G$.
