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 is proposed. The violation of the non-Abelian Bianchi identities (VNABI) Jμ is equal to Abelian-like monopole currents kμ defined by the violation of the Abelian-like Bianchi identities. Although VNABI is an adjoint operator satisfying the covariant conservation law DμJμ=0, it satisfies, at the same time, the Abelian-like conservation law μJμ=0. The Abelian-like conservation law μJμ=0 is also gauge-covariant. There are N2-1 conserved magnetic charges in the case of color SU(N). The charge of each component of VNABI is quantized à la Dirac. The color-invariant eigenvalues λμ of VNABI also satisfy the Abelian conservation law μλμ=0 and the magnetic charges of the eigenvalues are also quantized à la Dirac. If the color invariant eigenvalues condense in the QCD vacuum, each color component of the non-Abelian electric field Ea is squeezed by the corresponding color component of the solenoidal current Jμa. Then only the color singlets alone can survive as a physical state and non-Abelian color confinement is realized. This confinement picture is completely new in comparison with the previously studied monopole confinement scenario based on an Abelian projection after some partial gauge-fixing, where Abelian neutral states can survive as physical. To check if the scenario is realized in nature, numerical studies are done in the framework of lattice field theory by adopting pure SU(2) gauge theory for simplicity. Considering Jμ(x)=kμ(x) in the continuum formulation, we adopt an Abelian-like definition of a monopole following DeGrand-Toussaint as a lattice version of VNABI, since the Dirac quantization condition of the magnetic charge is satisfied on lattice partially. To reduce severe lattice artifacts, we introduce various techniques of smoothing the thermalized vacuum. Smooth gauge fixings such as the maximal center gauge (MCG), block-spin transformations of Abelian-like monopoles and extraction of physically important infrared long monopole loops are adopted. We also employ the tree-level tadpole improved gauge action of SU(2) gluodynamics. With these various improvements, we measure the density of lattice VNABI: ρ(a(β),n)=μ,sna(kμa(sn))2/(43Vnb3), where kμa(sn) is an n blocked monopole in the color direction a, n is the number of blocking steps, Vn=V/n4 (b=na(β)) is the lattice volume (spacing) of the blocked lattice. Beautiful and convincing scaling behaviors are seen when we plot the density ρ(a(β),n) versus b=na(β). A single universal curve ρ(b) is found from n=1 to n=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 since the scaling is obtained in all gauges adopted. The scaling, if it exists also for n→, shows that the lattice definition of VNABI has the continuum limit and the new confinement scenario is realized.