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 $J_{\mu }^a$. 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 $\rho (a(\beta ),n)=\sqrt{(k_n^1{)}^2+(k_n^2{)}^2+(k_n^3{)}^2}/(4\sqrt{4}V{b}^3)$, 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.

18 Pages with 18 figures: The revised version of arXiv:1712.05941.v1, Phys.Rev.D97, 034501 (2018). The proofs of the Dirac quantization condition and the simultaneous diagonalization of VNABI were incorrect. arXiv admin note: text overlap with arXiv:1402.1294

References in corpus (4)

• Duality of gauge field singularities and the structure of the flux tube in Abelian-projected SU(2) gauge theory and the dual Abelian Higgs model
• Monopoles, abelian projection, and gauge invariance
• Abelian dominance and the dual Meissner effect in local unitary gauges in SU(2) gluodynamics
• Gauge-independent Abelian mechanism of color confinement in gluodynamics

Cited by in corpus (7)

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• New Abelian-like monopoles and the dual Meissner effect
• Monopoles of the Dirac type and color confinement in QCD -- Study of the continuum limit
• Violation of non-Abelian Bianchi identity and QCD topology
• Direct and Indirect Methods of Vortex Identification in Continuum limit