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

Abstract

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} ~ 1.7 m_ρ, the lowest vector meson (the "rho meson") becomes massless, and it condenses (in addition to the pion condensate) for μ_I > 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_I > μ_{crit}.

33 pages, 7 figures; v2: references added, minor corrections; v3: added footnote about other possible condensate