Dual superconductivity and vacuum properties in Yang--Mills theories

We address, within the dual superconductivity model for color confinement, the question whether the Yang-Mills vacuum behaves as a superconductor of type I or type II. In order to do that we compare, for the theory with gauge group SU(2), the determination of the field penetration depth $\lambda$ with that of the superconductor correlation length $\xi$. The latter is obtained by measuring the temporal correlator of a disorder parameter developed by the Pisa group to detect dual superconductivity. The comparison places the vacuum close to the border between type I and type II and marginally on the type II side. We also check our results against the study of directly measurable effects such as the interaction between two parallel flux tubes, obtaining consistent indications for a weak repulsive behaviour. Future strategies to improve our investigation are discussed.