Inhomogeneous chiral symmetry breaking phases

In this thesis we investigate the formation of inhomogeneous chiral symmetry breaking phases, characterized by a spatially modulated quark-antiquark condensate. In order to determine the relevance of this kind of structure for the phase diagram of strongly interacting matter, we employ the Nambu-Jona-Lasinio model for two light quark flavors and study the properties of the ground state of the system. After observing the appearance of an inhomogeneous ''island'' at low temperatures and intermediate chemical potentials in the model phase diagram, we compare different one- and two-dimensional crystalline shapes for the chiral condensate, in order to determine which one is the thermodynamically most favored. Once having determined the favored shape for the ground state the system, we study in more detail the properties of this inhomogeneous phase. We then investigate the effects on it of common model extensions like the inclusion of vector interactions and an effective coupling with the Polyakov loop. Finally, in order to compare our results with recent predictions on inhomogeneous structures from quark ionic matter studies, we study the model phase structure at higher chemical potentials and determine that the favored shape for the system ground state changes. A careful discussion on the interpretation of these results is included as well.