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

TL;DR

This paper investigates rho meson condensation at finite isospin chemical potential using a holographic QCD model, revealing a phase transition where the rho meson becomes massless and condenses, breaking symmetries.

Contribution

It demonstrates rho meson condensation at finite isospin chemical potential within a holographic model, extending understanding of phase transitions in QCD-like theories.

Findings

Charged pion condenses at small chemical potential.

Rho meson becomes massless at critical chemical potential (~1.7 m_rho).

Rho meson condenses beyond the critical point, breaking symmetries.

Abstract

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} ~ 1.7 m_{\rho}, 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}.