Effective Degrees of Freedom at Chiral Restoration and the Vector Manifestation in HLS theory

The question as to what the relevant effective degrees of freedom at the chiral phase transition are remains largely unanswered and must be addressed in confronting both terrestrial and space laboratory observations purporting to probe matter under extreme conditions. We address this question in terms of the vector susceptibility \chi_V (VSUS in short) and the axial-vector susceptibility \chi_A (ASUS in short) at the temperature-induced chiral transition. We consider two possible, albeit simplified, cases that are contrasting, one that is given by the standard chiral theory where only the pions figure in the vicinity of the transition and the other that is described by hidden local symmetry (HLS) theory with the Harada-Yamawaki vector manifestation (VM) where nearly massless vector mesons also enter. We find that while in the standard chiral theory, the pion velocity v_\pi proportional to the ratio of the space component f_\pi^s of the pion decay constant over the time component f_\pi^t tends to zero near chiral restoration with f_\pi^t\neq 0, in the presence of the vector mesons with vanishing mass, the result is drastically different: HLS with VM {\it predicts} that \chi_V automatically equals \chi_A in consistency with chiral invariance and that v_\pi\sim 1$ with $f_\pi^t\approx f_\pi^s\to 0 as T\to T_c. These results are obtained in the leading order in power counting but we expect their qualitative features to remain valid more generally in the chiral limit thanks to the VM point.