Speaker
Description
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
$R_{\mathrm{DR}}~\equiv~\int d^{4}s~\mathrm{Tr}\left[A_{x}^{2}(s) + A_{y}^{2}(s) \right]$.
In the DR gauge, there remains a residual gauge symmetry for the gauge function $\Omega (t,z)$ like 2D QCD on the $tz$-plane. We define the ``$tz$-projection" as removal of $A_{x, y}(s) \to 0$. 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 $\beta = 6.0$. We find that the amplitude of two components $A_{x}(s)$ and $A_{y}(s)$ 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 $A_{t}(s)$ and $A_{z}(s)$ play a dominant role in quark confinement.
We calculate a spatial correlation $\langle \mathrm{Tr} A_{\perp}(s) A_{\perp}(s+ra_{\perp}) \rangle ~ (\perp = x,y)$ and estimate the spatial mass of $A_{\perp}(s) ~ (\perp = x,y)$ as $M \simeq 1.7 ~ \mathrm{GeV}$ in the DR gauge. It is conjectured that this large mass makes $A_{\perp}(s)$ inactive in the infrared region, which realizes the dominance of $A_{t}(s)$ and $A_{z}(s)$ in the DR gauge.
We also calculate spatial correlation of two temporal link-variables, and find that the correlation decreases as $\exp (-mr)$ with $m \simeq 0.6 ~ \mathrm{GeV}$, which corresponds to the correlation length $\xi \equiv 1/m \simeq 0.3 ~ \mathrm{fm}$. Using a rough approximation, 4D QCD is found to be regarded as an ensemble of 2D QCD systems with the coupling of $g_{\rm 2D} = gm$.
