Pion condensation in a soft-wall AdS/QCD model

Abstract

Abstract Finite isospin chemical potential μ I and temperature T have been introduced in the framework of soft-wall AdS/QCD model. By self-consistently solving the equation of motion, we obtain the phase boundary of pion condensation phase, across which the system undergoes a phase transition between pion condensation phase and normal phase. Compar- ing the free energy of solutions with and without pion condensation, we find that the phase transition is of first order type both at large μ I and small μ I . Qualitatively, the behavior at large μ I is in agreement with the lattice simulation in [6], while the behavior at small μ I is different from lattice simulations and previous studies in hard wall AdS/QCD model. This indicates that a full back-reaction model including the interaction of gluo-dynamics and chiral dynamics might be necessary to describe the small μ I pion condensation phase. This study could provide certain clues to build a more realistic holographic model.