Isospin QCD as a laboratory for dense QCD

QCD with the isospin chemical potential, $\mu_I$, is a useful laboratory to delineate the microphysics in dense QCD. To study the quark-hadron-continuity we use a quark-meson model that interpolates hadronic and quark matter physics at microscopic level. The equation of state is dominated by mesons at low density but taken over by quarks at high density. We extend our previous studies with two-flavors to the three-flavors case to study the impact of the strangeness which may be brought by kaons $(K_+, K_0) = (u\bar{s}, s\bar{d})$ and the U$_A$(1) anomaly. In the normal phase the excitation energies of kaons are reduced by $\mu_I$ in the same way as hyperons in nuclear matter at finite baryon chemical potential. Once pions condense, kaon excitation energies increases as $\mu_I$ does. Moreover, strange quarks become more massive through the U$_A$(1) coupling to the condensed pions. Hence at zero and low temperature the strange hadrons and quarks are highly suppressed. The previous findings in two-flavor models, sound speed peak, negative trace anomaly, gaps insensitve to $\mu_I$, persist in our three-flavor model and remain consistent with the lattice results to $\mu_I \sim 1$ GeV. We discuss the non-perturbative power corrections and quark saturation effects as important ingredients to understand the crossover equations of state measured on the lattice.