Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism.

Magnetic excitations play a crucial role in understanding the color confinement of 4D Yang-Mills theory, and we have the monopole and the center vortex as plausible candidates to explain its mechanism. Under suitable compactified setups of 4D Yang-Mills theory, we can achieve different weakly coupled descriptions of confinement phenomena: The monopole mechanism takes place on R^{3}×S^{1} with the double-trace deformation, and the center-vortex mechanism is effective on R^{2}×T^{2} with the 't Hooft flux. We unify these two semiclassical descriptions by showing the explicit relation between the monopole and center vortex.