Confinement Through a Two Dimensional Flux of the Thick Center Vortices

A two dimensional picture of the thick center vortex model is introduced. The spatial extent of the Wilson loop is oriented along the line with equation y = b x and the vortex movement is considered on the x ? y plane. A two-variable function with one free parameter a is considered as the vortex profile where a is proportional to the inverse of the vortex thickness. The potentials obtained from the two dimensional picture obey the N-ality dependence at large distances and Casimir scaling at intermediate distances. Furthermore, the concavity of the potentials corresponding to higher representations is slightly decreased in the two dimensional picture.