Connections between Thin,Thick and Projection Vortices in SU(2) Lattice   Gauge Theory
  We elucidate the connection between $SO(3) \times Z(2)$ and the usual SU(2) configuration variables. By exploiting the freedom of choosing a particular SO(3) representative we find a direct connection between the two configuration spaces. We are then able to compare the Kovacs-Tomboulis formulation of center vortices with the projection vortex formulation on the same configuration. Choosing a different representative, and going to the maximal center gauge, we show that projection vortices occur without approximation. The projection vortex dominance approximation results from dropping a factor in an exact expression for the Wilson loop. 
Richard W. Haymaker, Andrei Alexandru