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

We analyze the effect of an isospin chemical potential mu(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 mu(I) = mu(crit) similar to 1.7m(p), the lowest vector meson ( the "rho meson") becomes massless, and it condenses ( in addition to the pion condensate) for mu(I) > mu(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 mu(I) > mu(crit).