Numerical fractional instantons in SU(2): center vortices, monopoles, and a sharp transition between them

This is the authors' abstract. We don't add key points for this paper.

We use a numerical cooling algorithm to study fractional instantons in $SU(2)$ pure Yang-Mills on R²²_*, R³× S¹, and R× T²_* × S¹. We confirm that the fractional instantons are center vortices on R²²_* and monopoles on R³× S¹, and we calculate several properties relevant to using these solutions for semiclassical calculations. On R× T²_* × S¹, we interpolate between the large T²_* limit and the large S¹ limit to study how the solutions interpolate between center vortices and monopoles. We find that they are separated by a sharp transition, with 't Hooft's constant field strength solutions living at the transition point. These results contrast but do not contradict recent results suggesting continuity between vortices and monopoles.