Interaction of confining vortices in SU(2) lattice gauge theory

Center projection of SU(2) lattice gauge theory allows to isolate magnetic vortices as confining configurations. The vortex density scales according to the renormalization group, implying that the vortices are physical objects rather than lattice artefacts. Here, the binary correlations between points at which vortices pierce a given plane are investigated. We find an attractive interaction between the vortices. The correlations show the correct scaling behavior and are therefore physical. The range of the interaction is found to be (0.4±0.2) fm, which should be compared with the average planar vortex density of approximately 2 vortices/fm2. We comment on the implications of these results for recent discussions of the Casimir scaling behavior of higher dimensional representation Wilson loops in the vortex confinement picture.