  There are two distinct regimes of Yang-Mills theory where we can demonstrate
confinement, the existence of a mass gap, and fractional theta angle dependence
using a reliable semi-classical calculation. The two regimes are Yang-Mills
theory on $S^1 \times {\mathbb R}^3$ with a small circle and a double-trace
deformation, and Yang-Mills theory on $T^2 \times {\mathbb R}^2$ where the
torus $T^2$ is small and threaded by a 't Hooft flux. In the first case the
confinement mechanism is related to self-dual monopoles, whereas in the second
case self-dual center-vortices play a crucial role. These two topological
objects are distinct. In particular, they have different mutual statistics with
Wilson loops. On the other hand, they carry the same topological charge and
action. On ${\mathbb R \times T^2 \times S^1}$, we are able to extrapolate both
monopole regime and vortex regime to a quantum mechanical domain, where a
cross-over takes place. Both sides of the cross-over are described by a
deformed $\mathbb Z_N$ TQFT. On ${\mathbb R^2 \times S^1 \times S^1}$, we
derive the effective field theory of vortices from the effective theory of
monopoles in the presence of a 't Hooft flux. This results from a two-stage
adjoint Higgs mechanism, to $U(1)^{N-1}$ in 3d first and a $\mathbb Z_N$ EFT in
2d second. This proves adiabatic continuity of the two confinement mechanisms
across dimensions and shows how monopoles and their magnetic flux transmute
into center-vortices. This basic mechanism is flux fractionalization: The
magnetic flux of the monopoles fractionalizes and collimates in such a way that
2d Wilson loops detect it as a center vortex.
