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

Abstract

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 $\tilde{\sigma }\equiv \sqrt{⟨\sigma {⟩}^2+⟨{\pi }^a{⟩}^2}$ 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.

Comments: 5 pages, 3 Figures, to appear in the proccedings of the "Hadron2013" conference held in Nara, 4-8 November 2013