The structures of confining vortices which underlie pure $\mathrm{SU}\left(3\right)\mathrm{}$ Yang-Mills theory are studied by means of lattice gauge theory. Vortices and $Z_3$ monopoles are defined as dynamical degrees of freedom of the $Z_3$ gauge theory which emerges by center gauge fixing and by subsequent center projection. It is observed for the first time for the case of $\mathrm{SU}\left(3\right)\mathrm{}$ that these degrees of freedom are sensible in the continuum limit: the planar vortex density and the monopole density properly scales with the lattice spacing. By contrast to earlier findings concerning the gauge group $\mathrm{SU}\left(2\right),$ the effective vortex theory only reproduces 62% of the full string tension. On the other hand, however, the removal of the vortices from the lattice configurations yields ensembles with vanishing string tension. $\mathrm{SU}\left(3\right)\mathrm{}$ vortex matter which originates from Laplacian center gauge fixing is also discussed. Although these vortices recover the full string tension, they lack a direct interpretation as physical degrees of freedom in the continuum limit.

• Received 13 October 2003

DOI:https://doi.org/10.1103/PhysRevD.69.014503