Neutron star Neutron superfluid Proton superconductor Neutron vortex

Neutron star Neutron superfluid Proton superconductor Neutron vortex Proton vortex カラー超伝導 （ＣＦＬ相） カラー超伝導 ボルテックス

話の流れ 1. 導入部 2. vortex 3. Color-superconductor 4. Non-Abelian vortex と ＮＧモード 5. s-quark の質量 6. まとめと展望 レビュー 結果

２．vortex

Ginzburg-Landau theory • 超流動 • 超伝導

Vortex in dense QCD 高密度ＱＣＤのボルテックスは 超流動 カラー超伝導 両方の性質を持つ。 Semi-superfluid vortex と呼ばれている Balachandran-Digal-Matsuura (PRD 73, 074009)

３．Color-superconductor

Dense QCD (u, d, s) Alford-Rajagopal-Wilczek(‘ 98), Bailin-Love (‘ 84) 1. Weak coupling Asymptotic free: 2. Quark Cooper paring 3. color-superconductor(CSC) & color-flavor lock (CFL) SU(3)c is broken and color and flavor is locked.

Primary condensate: color/flavor/spin anti-symmetric Alford-Rajagopal-Wilczek(’ 98)

4. Non-Abelian vortex と ＮＧモード

Ginzburg-Landau Lagrangian Iida-Baym (PRD 63, 074018) Weak coupling QCD result

基底状態（order parameter space）

Superfluid vortex(triple) Forbes-Zhitnitsky (PRD 65, 085009), Iida-Baym (PRD 66, 014015) Semi-superfluid vortex (minimal) Balachandran-Digal-Matsuura (PRD 73, 074009)

Full numerical solution Gap increasing (m 1>m 8) Eto-Nitta (PRD 80, 125007)

Nambu-Goldstone mode vortex Nakano-Nitta-Matsuura (PRD 78, 054002)

Eto-Nakano-Nitta (PRD 80, 125011) moduli parameter moduli field Manton method Abelian vortex Non-Abelian vortex

Dynamics of non-Abelian NG mode Eto-Nakano-Nitta (PRD 80, 125011) CP(2) Lagrangian

Determination of Kahler class Shifman-Yung Ansatz (PRD 71, 045010) Kahler class (Lagrangian for ρ) Numerically solve EOM with vortex background FINITE! ⇒ normalizable mode

Strange quark mass and vortex stability So far we have considered asymptotically high density However, in a more realistic situation like neutron star, we should take an effect of strange masss into account. Iida-Matsuura-Tachibana-Hatsuda (PRL 93, 132001)

Strange quark mass is small but non-zero SU(3)C+L+R is approximate symmetry. CP 2 NG zero mode becomes slightly massive An effective potential in CP 2 vortex theory Eto-Nitta-Yamamoto (PRL) Massless CP 2 NLSM ⇒ massive CP 2 NLSM

low high

Future directions • Glitch phenomena of neutron star • Vortex-particle scattering => cooling mechanism • Connection of superfluid vortex in hadronic matter and non-Abelian vortex in quark matter • Quark-Hadron continuity (duality) • Monople and confinment

Quark-Hadron continuity (duality) Phase Interaction NG Vector Fermion (Skyrmion) Condensate mechanism confinement Low density Confinement Strong 8 Meson 9 Baryon 8 Baryon Monopole Dual Missner Quark High density Higgs Weak 8+1 Gluon 8 Quark 9 Quark Diquark Missner D E Monopole NT A