Equation of state in the pion condensation phase in the asymmetric nuclear matter using a holographic QCD model

We study the asymmetric nuclear matter using a holographic QCD model by introducing a baryonic charge in the infrared boundary. We first show that, in the normal hadron phase, the predicted values of the symmetry energy and it's slope parameter are comparable with the empirical values. We find that the phase transition from the normal phase to the pion condensation phase is delayed compared with the pure mesonic matter: The critical chemical potential is larger than the pion mass which is obtained for the pure mesonic matter. We also show that, in the pion condensation phase, the pion contribution to the isospin number density increases with the chemical potential, while the baryonic contribution is almost constant. Furthermore, the value of chiral condensation implies that the enhancement of the chiral symmetry breaking occurs in the asymmetric nuclear matter as in the pure mesonic matter. We also give a discussion on how to understand the delay in terms of the 4-dimensional chiral Lagrangian including the rho and omega mesons based on the hidden local symmetry.