Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography

The spectra of pions-known as the pseudo-Goldstone bosons of spontaneous chiral symmetry breaking-and their relationship with the chiral and pion superfluidity phase transitions have been investigated in the framework of soft-wall AdS/QCD. We prove that pions are massless Goldstone bosons in the chiral limit even at finite temperature, which was usually considered an assumption in soft-wall models. Above T-c, at which the chiral condensate vanishes, the spectra of pions and scalar mesons merge, showing evidence of restored chiral symmetry at the hadronic spectrum level. Extending to finite quark mass, pion masses increase with quark mass. Further, it is more interesting to observe that the pole masses of pions decrease with temperature below T-c, which agrees with the analysis by Son and Stephanov [Phys. Rev. Lett. 88, 202302 (2002)]. Meanwhile, symmetry restoration above T-c could be seen in the scalar and pseudoscalar meson spectra. With finite temperature and isospin chemical potential mu(I), we show that the masses of charged pions are split. The mass of a positively charged pion pi(+) decreases almost linearly to zero when mu(I) grows to its critical value mu(c)(I), where pion condensation begins. This reveals the Goldstone nature of pi(+) after the pion superfluidity transition, which is closely related to experimental observations.