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Inhomogeneous chiral condensates in three-flavor quark matter

We investigate the effect of strange quark degrees of freedom on the formation of inhomogeneous chiral condensates in a three-flavor Nambu--Jona-Lasinio model in mean-field approximation. A Ginzburg-Landau study complemented by a stability analysis allow us to determine in a general way the location of the critical and Lifshitz points, together with the phase boundary where the (partially) chirally restored phase becomes unstable against developing inhomogeneities, without resorting to specific assumptions on the shape of the chiral condensate. We discuss the resulting phase structure and study the influence of the bare strange-quark mass $m_s$ and the axial anomaly on the size and location of the inhomogeneous phase compared to the first-order transition associated with homogeneous matter. We find that, as a consequence of the axial anomaly, critical and Lifshitz point split. For realistic strange-quark masses the effect is however very small and becomes sizeable only for small values of $m_s$.