Abstract
We investigate the Abelian dual Meissner effect due to violation of the non-Abelian Bianchi identity in SU (3) gauge thoery without gauge fixing. To decide the vacuum type, we evaluate the Ginzburg-Landau parameter from the spatial distribution of color electric fields and squared monopole density. Although the study is done only on 24 (40)3 × 4 lattice at β = 5.6, the SU (3) vacuum is found to be of the type 1 near the border of type 1 and type 2. We also confirm the dual Ampere’s law directly.
Highlights
Quark confinement mechanism is one of the most important problem in particle physics [1]
The idea of the dual superconducting picture is very interesting in understanding the mechanism of confinement, in constract to SUSY QCD [4] or GeorgiGlashow model [5, 6] with scalar fields, it is not straightforward to define monopoles in QCD
In the previous work [17] studying the spatial distribution of color electric fields and monopole currents, they used the connected correlations between a non-Abelian Wilson loop and Abelian operators in S U(2) gauge theory without gauge fixing
Summary
Quark confinement mechanism is one of the most important problem in particle physics [1]. One of the authors (T.S.) found that the violation of the non-Abelian Bianchi identity(VNABI) is equal to Abelian-like monopoles in the continuum theory [12]. This idea is similar to the Dirac monopole [13] in U(1) quantum electrodynamics. We discuss the Abelian dual Meissner e↵ect due to VNABI in S U(3) gauge theory. Abelian monopole current squeezes the Abelian color electric field as a solenoidal current These results agree with the dual superconducting picture. In the case of S U(3) gauge theory, VNABI is regarded as eight Abelian-like monopoles in the continuum QCD. This definition (4) satisfies the Abelian conservation condition and takes an integer value which corresponds to the magnetic charge obeying the Dirac quantization condition [18]
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