Quark Matter in a Strong Magnetic Background

In this chapter, we discuss several aspects of the theory of stronginteractions in presence of a strong magnetic background. In particular, wesummarize our results on the effect of the magnetic background on chiralsymmetry restoration and deconfinement at finite temperature. Moreover, wecompute the magnetic susceptibility of the chiral condensate and the quarkpolarization at zero temperature. Our theoretical framework is given by chiralmodels: the Nambu-Jona-Lasinio (NJL), the Polyakov improved NJL (or PNJL) andthe Quark-Meson (QM) models. We also compare our results with the ones obtainedby other groups.