Heavy quark interactions in extreme conditions

The research project have been devoted to the study of the properties of strong interactions in the extreme conditions represented by the presence of large magnetic fields or non-zero baryon density. These scenarios have a important role in the phenomenology of several physical systems, ranging from the conditions expected in the early stage of the Universe to those recreated in heavy ion collision experiments. In this context, the great and relevant interest in probing the modifications arising in the non-perturbative properties of QCD is successfully supplied by the lattice framework, which represents a reliable tool for the study of the features of the theory. In the first part, we focused on the effects due to large external magnetic fields on the $Q\bar{Q}$ potential. An in-depth investigation at zero temperature allowed to observe that the interaction between a quark-antiquark pair becomes anisotropic, this effect essentially due to the modification of the string tension. Results also agree with a speculative scenario in which an anisotropic deconfinement may take place at very large magnetic fields. The analysis generalized at higher temperatures allowed to describe the fate of the potential when the pseudo-critical temperature $T_c$ is reached from below. The observed clear loss of the deconfining properties agrees with the picture of a decreasing $T_c$ in the presence of a magnetic field, suggesting to to understand it in terms of a sort of deconfinement catalysis. A step forward has been done by looking at the effects of the external field on the interaction in the high-$T$ region. In the QGP phase, the study of the modification of the screening masses allowed to show that also here an anisotropy is present, but also that their value tends to increase when $|e|B$ grows. Again, also in this case the observed effects agree with the picture of a decreasing critical temperature $T_c$, the system pushed to the more and more deconfined region as the magnetic field becomes greater. Next, screening properties have been investigated in the presence of a non-zero baryon density. A generalization of the non-perturbative definition of the color-screening masses has been proposed and used to probe the effects on them. The observed increasing of both the masses induced by $\mu_B$ evidences the role of the chemical potential as a parameter driving the system far from the transition. Moreover, the study has been extended in the phase diagram with imaginary chemical potential, looking at the peculiar behaviour of the observables near the Roberge-Weiss transition. Finally, confining properties of the theory through have been studied through the single quark free energy $F_Q$ at finite density. Interesting results have been found in the behaviour of a new observable: the Polyakov loop susceptibility $\chi_{Q,\mu_B}$, coinciding with the second derivative of the single quark free energy $F_Q$ with respect to the baryon chemical potential. A preliminary investigation shows that this object has a clear peak at $T_c$~150MeV, making it a promising observable characterizing the confined-deconfined transition.