A new scheme for color confinement and violation of the non-Abelian Bianchi identities

Abstract

A new scheme for color confinement in QCD due to violation of the non-Abelian Bianchi identities proposed earlier is revised. The violation of the non-Abelian Bianchi identities (VNABI) $J_μ$ is equal to Abelian-like monopole currents $k_μ$ defined by the violation of the Abelian-like Bianchi identities. VNABI satisfies $\partial_μJ_μ=0$. There are $N^2-1$ conserved magnetic charges in $SU(N)$ QCD. The charge of each component of VNABI is assumed to satisfy the Dirac quantization condition. %%%%% Each color component of the non-Abelian electric field $E^a$ is squeezed by the corresponding color component of the solenoidal current $J^a_μ$. Then only the color singlets alone can survive as a physical state and non-Abelian color confinement is realized. Numerical studies are done in the framework of $SU(2)$ lattice gauge theory. We adopt an Abelian-like definition of monopole following DeGrand-Toussaint as a lattice version of VNABI. To reduce severe lattice artifacts, we introduce various techniques of smoothing the thermalized vacuum such as the maximal center gauge (MCG) fixing. We measure the density $ρ(a(β),n)=\sqrt{(k_n^1)^2+(k_n^2)^2+(k_n^3)^2}/(4\sqrt{4}Vb^3)$, where $k_n^a$ is an $n$ blocked monopole in the color direction $a$ and $b=na(β)$ is the blocked lattice spacing. Beautiful scaling behaviors are seen when we plot $ρ(a(β),n)$ versus $b=na(β)$. A single universal curve $ρ(b)$ is found from $n=1\sim 12$, which suggests that $ρ(a(β),n)$ is a function of $b=na(β)$ alone. The universal curve seems independent of a gauge fixing procedure used to smooth the lattice vacuum when the scaling is obtained. The scaling shows that the lattice definition of VNABI has the continuum limit.