Renormalization-Group Flow Analysis of Meson Condensations in Dense Matter

We present a renormalization-group (RG) flow argument for s-wave kaon condensation in dense nuclear-star matter predicted in chiral perturbation theory. It is shown that it is the {\it relevant} mass term together with {\it any} attractive interaction for the kaon in medium that triggers the instability. We show that a saddle point of multi-dimensional RG flow can imply a phase transition. Pion condensation is also analyzed along the same line of reasoning.