Inhomogeneous instabilities in high-density QCD

QCD at large densities exhibits a moat regime in the scalar-pseudoscalar sector. The resolution of its dynamics is pivotal for the access to the onset of new phases including the potential critical endpoint of QCD. In this work we present the first selfconsistent analysis of this regime with the functional renormalisation group approach to QCD. We map out the moat regime, including a first analysis of potential inhomogeneous instabilities at baryon chemical potential ${\mu }_B\gtrsim 600$ MeV on the chiral crossover line.