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Phases and condensates in zero-temperature QCD at finite $μ_I$ and $μ_S$

I discuss pion and koan condensation and the the properties of the phases of QCD at finite isospin chemical potential $μ_I$ and strangeness chemical potential $μ_S$ at zero temperature using three-flavor chiral perturbation theory. Electromagnetic effects are included in the calculation of the phase diagram, which implies that the charged meson condensed phases become superconducting phases of QCD with a massive photon via the Higgs mechanism. Without electromagnetic effects, we show results for the light quark condensate and the pion condensate as functions of $μ_I$ at next-to-leading (NLO) order in the low-energy expansion. The results are compared with recent lattice simulations and by including the NLO corrections, one obtains very good agreement.