• center symmetry
• confinement
• lattice qcd
• monte-carlo methods

In the first of the thesis, we performed a numerical investigation of trace-deformed Yang-Mills theory, in which the deconfinement phase transition is avoided by forbidding the spontaneous symmetry breaking of center symmetry. We found that the both the spectrum and the topological properties of the deformed theory and the usual confining YM are the same, as soon as center symmetry is recovered. We also studied the transition from the deconfined to the re-confined phase by looking at the localization properties of Dirac eigenmodes and thermal monopoles behaviour across the transition.
In the second part, we considered QCD with dynamical fermions; in particular we computed the localization properties of the Dirac eigenmodes across the Roberge-Weiss transition, i.e. when an imaginary chemical potential is added to QCD action. The final part of this thesis regards the study of thermal monopoles across the deconfinement crossover in full QCD.