The Critical Scale of the Dual Superconductor Picture of QCD

The nonperturbative phenomena of QCD like color confinement is well described through the dual superconductor picture in the Maximally Abelian (MA) gauge. In this gauge, monopoles appear as important degrees of freedom composed by nonabelian gauge fields. We investigate the peculiar size $R_c$ of the monopole in the MA gauge, considering the theoretical similarity between spinglass and the MA gauge fixing. As for the properties at larger scale than the monopole size $R_c$, the system can be described by the dual superconductor theory with local abelian fields. At shorter distances than $R_c$, such a dual Higgs theory should be treated as a non-local field theory, and therefore one must take another framework like the perturbative QCD. Thus, the monopole size gives a critical scale on the change of the theoretical structure of QCD.