Rho meson condensation at finite isospin chemical potential in a holographic model for QCD

We analyze the effect of an isospin chemical potential μ _I in the Sakai-Sugimoto model, which is the string dual of a confining gauge theory related to large N _c QCD, at temperatures below the chiral symmetry restoration temperature. For small chemical potentials we show that the results agree with expectations from the low-energy chiral Lagrangian, and the charged pion condenses. When the chemical potential reaches a critical value μ _I = μ _crit 1.7m _ρ, the lowest vector meson (the ''rho meson'') becomes massless, and it condenses (in addition to the pion condensate) for μ ₁>μ _crit. This spontaneously breaks the rotational symmetry, as well as a residual U(1) flavor symmetry. We numerically construct the resulting new ground state for μ ₁μ _crit.