Abstract
Finite isospin chemical potential μI 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 μI and small μI. Qualitatively, the behavior at large μI is in agreement with the lattice simulation in [6], while the behavior at small μI 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 μI pion condensation phase. This study could provide certain clues to build a more realistic holographic model.
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