Dimensional reduction gauge and effective dimensional reduction in the four dimensional Yang-Mills theory
當銘 啓
京都大学
日時：2024年06月18日（火） 15:30-
場所：原子核理論セミナー室（総合研究棟10階1021号室）
In four-dimensional (4D) QCD, quark confinement is characterized by one-dimensional color-electric flux tube formation, which leads to a linear interquark potential. The flux-tube formation implies a possibility of low-dimensionalization of 4D QCD. We propose a new gauge fixing of “dimensional reduction (DR) gauge” defined so as to minimize RDR ≡ ∫ d^4 s Tr [ Ax(s)^2 + Ay(s)^2 ] . In the DR gauge, there remains a residual gauge symmetry for the gauge function Ω(t, z) like 2D QCD on the tz-plane. We define the “tz-projection” as removal of Ax,y(s) → 0. After the tz-projection in the DR gauge, 4D QCD is regarded as an ensemble of 2D QCD-like systems on the tz-plane, which are piled in the x and y directions and interact with neighboring planes. We also formulate the DR gauge and the tz-projection on lattice, and investigate low-dimensionalization in SU(3) lattice QCD at β = 6.0. We find that the amplitude of two components Ax(s) and Ay(s) are strongly suppressed in the DR gauge. In the DR gauge, the interquark potential is not changed by the tz-projection, and the two components At(s) and Az(s) play a dominant role in quark confinement. We calculate a spatial correlation ⟨TrA⊥(s)A⊥(s + ra⊥)⟩ (⊥= x, y) and estimate the spatial mass of A⊥(s) (⊥= x, y) as M ≃ 1.7 GeV in the DR gauge. It is conjectured that this large mass makes A⊥(s) inactive in the infrared region, which realizes the dominance of At(s) and Az(s) in the DR gauge. We also calculate spatial correlation of two temporal link-variables, and find that the correlation decreases as exp(−mr) with m ≃ 0.6 GeV, which corresponds to the correlation length ξ ≡ 1/m ≃ 0.3 fm. Using a rough approximation, 4D QCD is found to be regarded as an ensemble of 2D QCD systems with the coupling of g2D = gm.