Inhomogenuous instabilities at large chemical potential in a rainbow-ladder QCD model

In this work we continue our efforts to study the existence of a phase with an inhomogeneous, i.e., spatially varying, chiral condensate in QCD. To this end we employ a previously established method of stability analysis of the two-particle irreducible effective action in a truncation that corresponds to a rainbow-ladder approximation of the quark-gluon interaction of QCD. If the analysis is restricted to homogeneous phases, the phase diagram features a first-order chiral transition in the lower-temperature regime. Performing the stability analysis along the lower-chemical-potential border of the corresponding spinodal region, we find that below a certain temperature the homogeneous chirally symmetric solution is unstable against inhomogeneous condensation. We argue that this instability may persist to chemical potentials above the homogeneous first-order phase boundary, in which case it signals the existence of an inhomogeneous ground state. Our methodology is also applicable for more sophisticated truncations of the QCD effective action.