Inhomogeneous phases and the Moat Regime in Nambu-Jona-Lasinio-Type models

This thesis investigates exotic phases within effective models for strongly interacting matter. The focus lies on the chiral inhomogeneous phase (IP) that is characterized by a spontaneous breaking of translational symmetry and the moat regime, which is a precursor phenomenon exhibiting a non-trivial mesonic dispersion relation. These phenomena are expected to occur at non-zero baryon densities, which is a parameter region that is mostly non-accessible to first-principle investigations of Quantum chromodynamics (QCD). As an alternative approach, we consider the Gross-Neveu (GN) and Nambu-Jona-Lasinio (NJL) model within the mean-field approximation, which can be regarded as effective models for QCD. We focus on two aspects of the moat regime and the IP in these models. First, we investigate the influence of the employed regularization scheme in the (3+1)-dimensional NJL model, which is nonrenormalizable, i.e., the regulator cannot be removed. We find that the moat regime is a robust feature under change of regularization scheme, while the IP is sensitive to the specific choice of scheme. This suggests that the moat regime is a universal feature of the phase diagram of the NJL model, while the IP might only be an artifact of the employed regulator. Second, we study the influence of the number of spatial dimensions on the emergence of the IP. To this end, we investigate the GN model in noninteger spatial dimensions d. We find that the IP and the moat regime are present for d < 2, while they are absent for d > 2. This demonstrates the central role of the dimensionality of spacetime and illustrates the connection of previously obtained results in this model in integer number of spatial dimensions. Moreover, this suggests that the occurrence of these phenomena in three spatial dimensions is solely caused by the finite regulator. In summary, this thesis contributes to advancing our understanding of the phase structure of QCD, particularly regarding the existence and characteristics of inhomogeneous phases and the moat regime. Even though the investigations are performed within effective models, they provide valuable insight into the aspects that are crucial for the formation of an inhomogeneous chiral condensate in fermionic theories.