Pion condensation phase at finite isospin chemical potential in a Holographic QCD model

We summarize main points of our recent work where we studied the pion condensation for non-zero isospin chemical potential within a holographic QCD model. We confirmed that the second order phase transition with the mean field exponent occurs when the isospin chemical potential $\mu_I$ exceed the pion mass, which is consistent with the result obtained by the chiral effective Lagrangian at $O(p^2)$. We find that a deviation for large $\mu_I$ region can be understood as a higher order effects in the chiral effective Lagrangian. Our result shows that the chiral condensate defined by $\tilde{\sigma} \equiv \sqrt{ \langle \sigma \rangle^2 + \langle \pi^a \rangle^2 }$ is almost constant in the small $\mu_I$ region, while it grows with $\mu_I$ in the large $\mu_I$ region showing an enhancement of the chiral symmetry breaking.