  In a common paradigm, the electronic structure of condensed matter is divided
into weakly and strongly correlated compounds. While conventional band theory
usually works well for the former class, many-body effects are essential for
the latter. Materials like the familiar SrTiO$_3$ compound that bridge or even
abandon this characterization scheme are highly interesting. Here it is shown
by means of combining density functional theory with dynamical-mean field
theory that oxygen vacancies on the STO (001) surface give rise to a dichotomy
of weakly-correlated $t_{2g}$ low-energy quasiparticles and localized 'in-gap'
states of dominant $e_g$ character with subtle correlation signature. We
furthermore touch base with recent experimental work and study the surface
instability towards magnetic order.
