Vortices, Confinement

We review lattice evidence for the vortex mechanism of quark confinement and study the influence of charged matter fields on the vortex distribution. 1 Review of the vortex mechanism of quark confinement In the early days of QCD some people argued that quarks are confined due to the non-abelian nature of gauge-fields leading to attraction between flux-lines. But the abelian U(1) lattice gauge theory in four dimensions has also a confining phase. Therefore, it seems more reasonable to argue that the QCD vacuum is non-trivial, a condensation of topological objects which expel the color electric flux of test charges Q. We have therefore to answer the question which type of large scale topological fluctuations determines the infrared behavior of the Q ¯ Q-potential. To find an appropriate reply we have to specify more exactly which charges are confined in an SU(N) gauge theory. A fast first answer, SU(N) color charges, is not correct since adjoint charges are not confined, they are screened by the confining medium. Dual superconductor models derive from the confinement mechanism of U(1) that all abelian charges are confined. But we know that charges with N-ality zero are screened. Finally, we can conclude that charges with non-vanishing N-ality are confined and N-ality zero loops are not disordered. In the infrared the asymptotic string tension depends only on the N-ality of the charges.