Transition of a spherical vortex to a Dirac monopole with fractional topological charge

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We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. We find some evidence for fractional topological charge during cooling the spherical center vortex on a [Formula: see text] lattice. We identify the object with topological charge [Formula: see text] as a Dirac monopole with a gauge field fading away at large distances. Therefore, even for periodic boundary conditions, it does not need an anti-monopole.