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) $J_{\mu}$ is equal to Abelian-like monopole currents $k_{\mu}$ defined by the violation of the Abelian-like Bianchi identities. VNABI satisfies $\partial_{\mu}J_{\mu}=0$. 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 $J^a_{\mu}$. 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 $\rho(a(\beta),n)=\sqrt{(k_n^1)^2+(k_n^2)^2+(k_n^3)^2}/(4\sqrt{4}Vb^3)$, where $k_n^a$ is an $n$ blocked monopole in the color direction $a$ and $b=na(\beta)$ is the blocked lattice spacing. Beautiful scaling behaviors are seen when we plot $\rho(a(\beta),n)$ versus $b=na(\beta)$. A single universal curve $\rho(b)$ is found from $n=1\sim 12$, which suggests that $\rho(a(\beta),n)$ is a function of $b=na(\beta)$ 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.