The Vector and Axial-Vector Susceptibilities and Effective Degrees of Freedom in the Vector Manifestation

The question as to what the relevant degrees of freedom are at the thermal chiral phase transition is addressed in terms of the “vector manifestation (VM)” of chiral symmetry à la Harada and Yamawaki. We find that both the vector susceptibility χV and the axial-vector susceptibility χA at the chiral transition require other degrees of freedom than pions in the chiral limit. The possible candidates are zero-mass vector mesons and quasiquarks. In the presence of these degrees of freedom, hidden local symmetry (HLS) theory with vector manifestation predicts that χV equals χA in consistency with chiral invariance and that both the time component f t π and the space component f s π of the pion decay constant vanish at the chiral phase transition. With the VM, the pion velocity vπ proportional to f s π/f t π at T = Tc is predicted to be equal to 1. and Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208 and School of Physics, Korea Institute for Advanced Study, Seoul 130-012, Korea.