We investigate the connection between color confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the confinement/deconfinement temperature is approached from above. In particular, we study the distribution of monopole currents with multiple wrappings in the Euclidean time direction, corresponding to two or more particle permutations, and show that multiple wrappings increase as the deconfinement temperature is approached from above, in a way compatible with a condensation of such objects happening right at the deconfining transition. We also address the question of the thermal monopole mass, showing that different definitions give consistent results only around the transition, where the monopole mass goes down and becomes of the order of the critical temperature itself

We investigate the properties of thermal abelian magnetic monopoles in the high temperature phase of Yang-Mills theories, following a recent proposal for their identification on lattice configurations. The study is done for SU(2) pure gauge theory, for temperatures going up to about 10 times the deconfining temperature and using the Maximal Abelian gauge to perform the abelian projection. We find that the monopole density has a well defined continuum limit. Its temperature dependence disagrees with a free particle gas prediction and is instead well described by a T 3 /(log(T /Λ)) α behaviour in all the explored range, with α ∼ 2 and Λ ∼ 100 MeV. Also the study of spatial correlations of thermal monopoles shows the presence of non-trivial interactions among them. Finally, we discuss the gauge dependence of our results, showing that it is significant and that, even within the Maximal Abelian gauge, Gribov copy effects are important.

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 λ with that of the superconductor correlation length ξ. 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.

We review recent lattice results, concerning the properties and the role of thermal abelian magnetic monopoles in the high temperature phase of Yang-Mills theories, and discuss preliminary evidence for the onset of their condensation as the deconfining temperature is approached from above.

Within the dual superconductor model for the QCD vacuum we compare the field penetration depth λ with the correlation length ξ of the Higgs condensate. The comparison places the vacuum marginally on the type II side. A qualitative check of the interaction between two parallel flux tubes gives also consistent indications for a weak repulsive behaviour