Dimensional reduction gauge and effective dimensional reduction in the four-dimensional Yang-Mills theory

Abstract

Motivated by one-dimensional color-electric flux-tube formation in four-dimensional (4D) QCD, we investigate a possibility of effective dimensional reduction in the 4D Yang-Mills (YM) theory. We propose a new gauge fixing of "dimensional reduction (DR) gauge" defined so as to minimize $R_{\mathrm{DR}}\equiv \int d^{4}s\mathrm{Tr}\left[A_x^2(s)+A_y^2(s)\right]$, which has a residual gauge symmetry for the gauge function $\Omega (t,z)$ like 2D QCD on the $t$-$z$ plane. We investigate effective dimensional reduction in the DR gauge using SU(3) quenched lattice QCD at $\beta =6.0$. The amplitude of $A_x(s)$ and $A_y(s)$ are found to be strongly suppressed in the DR gauge. We consider "$tz$-projection" of $A_{x,y}(s)\to 0$ for the gauge configuration generated in the DR gauge, in a similar sense to Abelian projection in the maximally Abelian gauge. By the $tz$-projection in the DR gauge, the interquark potential is not changed, and $A_t(s)$ and $A_z(s)$ play a dominant role in quark confinement. In the DR gauge, we calculate a spatial correlation $⟨\mathrm{Tr}{A}_{\perp }(s)A_{\perp }(s+r{a}_{\perp })⟩(\perp =x,y)$ and estimate the spatial mass of $A_{\perp }(s)(\perp =x,y)$ as $M\simeq 1.7\mathrm{GeV}$. It is conjectured that this large mass makes $A_{\perp }(s)$ inactive and realizes the dominance of $A_t(s)$ and $A_z(s)$ in infrared region in the DR gauge. We also calculate the spatial correlation of two temporal link-variables and find that the correlation decreases as $\exp (-mr)$ with $m\simeq 0.6\mathrm{GeV}$. Using a crude approximation, the 4D YM theory is reduced into an ensemble of 2D YM systems with the coupling of $g_{2D}=gm$.

15 pages, 11 figures

References in corpus (18)

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Center Dominance and Z2 Vortices in SU(2) Lattice Gauge Theory
• Locality and exponential error reduction in numerical lattice gauge theory
• Detailed Analysis of the Three Quark Potential in SU(3) Lattice QCD
• Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in the Maximally Abelian Gauge in Lattice QCD
• Infrared Features of the Landau Gauge QCD
• Chiral Symmetry Breaking in Abelian-Projected SU(2) Lattice Gauge Theory
• Flux Tubes of Two- and Three-Quark System in Full QCD
• Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function
• Distribution of Stress Tensor around Static Quark--Anti-Quark from Yang-Mills Gradient Flow
• Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in Maximally Abelian Gauge in SU(3) Lattice QCD
• Perfect Abelian dominance of quark confinement in SU(3) QCD
• Three-quark potential and Abelian dominance of confinement in SU(3) QCD
• Semi-analytical Proof of Abelian Dominance on Confinement in the Maximally Abelian Gauge
• Instantaneous Interquark Potential in Generalized Landau Gauge in SU(3) Lattice QCD: A Linkage between the Landau and the Coulomb Gauges
• Instantaneous interquark potential in generalized Landau gauge in SU(3) lattice QCD: a possible gauge for the quark potential model
• Clear correlation between monopoles and the chiral condensate in SU(3) QCD

Cited by in corpus (1)

• Color-magnetic correlations in SU(2) and SU(3) lattice QCD