Strings and Aharonov–Bohm effect in Abelian Higgs model

We investigate numerically the properties of the Abrikosov–Nielsen–Olesen strings in 4D Abelian Higgs model. The fractal dimension Df of the vortex strings was found to be large in the Coulomb phase and it is close to 2 in the Higgs phase. We also show that the Wilson loop for non-integer charges is correlated with the linking number of the vortex string world sheets and the test particle world trajectory. We find that this topological (Aharonov–Bohm) interaction gives the main contribution to the Wilson loop quantum average for non-integer test charges in the vicinity of the Coulomb–Higgs phase transition.