A new scheme for color confinement due to 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 is discussed. 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. Although VNABI is an adjoint operator satisfying the covariant conservation rule $D_{\mu }{J}_{\mu }=0$, it gives us, at the same time, the Abelian-like conservation rule ${\partial }_{\mu }{J}_{\mu }=0$. The Abelian-like conservation rule ${\partial }_{\mu }{J}_{\mu }=0$ is also gauge-covariant. There are $N^2-1$ conserved magnetic charges in the case of color $SU(N)$. The charge of each component of VNABI is quantized à la Dirac. VNABI satisfying the Dirac quantization condition could be defined on lattice as lattice Abelian-like monopole currents without any gauge-fixing. Previous studies of the Abelian-like monopoles $k_{\mu }$ on lattice show that non-Abelian color confinement could be understood by the Abelian-like dual Meissner effect due to condensation of VNABI.

Comments: 5 pages, 1 figure