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Phase diagram of strongly interacting matter under strong magnetic fields

The understanding of the behaviour of strongly interacting matter at finite temperature and density is of fundamental interest and has applications in cosmology, in the astrophysics of neutron stars and in the physics of relativistic heavy ion collisions. Given the possible existence of strong magnetic fields in the mentioned situations, their effect on the QCD phase diagram has recently become a topic of increasing interest. Here, we report on the study of this issue in the framework of the two flavor Nambu-Jona-Lasinio model with Polyakov loop (PNJL) and an extension of it, the so-called entangled PNJL model (EPNJL).