New Pattern of Chiral Symmetry Restoration ∗

In this talk I summarize our recent works on the chiral symmetry restoration in the large flavor QCD using the hidden local symmetry (HLS) as an effective field theory of QCD. Bare parameters in the HLS are determined by matching the HLS with QCD at the matching scale through the Wilsoninan matching conditions. This Wilsonian matching leads to the vector manifestation of the Wigner realization of the chiral symmetry in which the symmetry is restored by the massless degenerate pion (and its flavor partners) and rho meson (and its flavor partners) as the chiral partner. Chiral symmetry restoration in the large flavor QCD is an interesting subject to study. In Ref. [4] an IR fixed point was found to exist at two-loop beta function for large Nf (< 11 2 Nc) in the QCD with massless Nf flavors. Based on this IR fixed point, it was found [5] through the modified ladder Schwinger-Dyson equation that chiral symmetry restoration in fact takes place for Nf such that N cr f < Nf < 11 2 Nc, where N cr f ≃ 4Nc(= 12 for Nc = 3). Moreover, the lattice simulation indicates that the chiral restoration does occur at N cr f ≈ 7 [6]. In Ref. [1] we pointed that the chiral restoration takes place for large Nf also in the hidden local symmetry (HLS) [7] by its own dynamics. The inclusion of the quadratic divergences in the renormalization group equations (RGE’s) was essential to obtain the phase transition. This inclusion is also necessary when we match the HLS with the underlying QCD through the Wilsonian matching which is shown to work very well for the realistic case of Nf = 3. [2] In Ref. [3] we applied the Wilsonian matching for the large flavor QCD, and proposed “Vector Manifestation (VM)” of the chiral symmetry as a novel manifestation of the Wigner realization in which the vector meson denoted by ρ (ρ meson and its flavor partner) becomes massless at the chiral phase transition point. Accordingly, the (longitudinal) ρ becomes the chiral partner of the Nambu-Goldstone (NG) boson denoted by π (pion and its flavor partners). In this talk I summarize the Wilsonian matching and the VM. For details please see Refs. [1, 2, 3]. Let me start from the Wilsonian matching of the HLS with QCD proposed in Ref. [2]. In the HLS axialvector and vector current correlators are well described by the tree contributions with including O(p4) terms † when the momentum is around the matching scale, Q2 ∼ Λ2: Π (HLS) A (Q ) = F 2 π (Λ) Q2 − 2z2(Λ) , Π (HLS) V (Q ) = F 2 σ (Λ) [