Confinement inSU(N)lattice gauge theories

The behavior of the Wilson and 't Hooft loops, and of the electric- and magnetic-flux free energies, is examined in weak-coupling $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ lattice gauge theories. The ability of thin tubes of magnetic flux to spread into thick flux tubes is emphasized as the key feature which is required for confinement. While control over the energetics of these fluctuations sufficient to prove confinement is still lacking, we are able to prove that if constraints are inserted which prevent this spreading of $Z\left(N\right)\mathrm{}$ magnetic flux then nonconfining behavior results.