Gauge independence of Abelian confinement mechansim in SU

Gauge independence of Abelian confinement mechansim in SU 2 gluodynamics T. Suzuki, Kanazawa Univ. , Japan (In collab. with T. Sekido, K. Ishiguro, Y. Koma) Lattice 2007 -- ---31/7/2007

Surprizing results: 1. 2. 3. 4. Extraction of the confining component in gauge fields is possible without cooling or any gauge fixing. Gauge independence Abelian and monopole dominances are almost perfect. Squeezing of electric fields occurs due to solenoidal monopole currents. The Abelian dual Meissner effect is working. The vacuum is near the border between type 1 and 2 superconductor. Confinement of non-Abelian color charge is explained in the framework of the Abelian dual Meissner effect.

1. Extraction of confining component Non-perturbative confining component

2 -1. Abelian dominance

Abelian static potential Error bars are very small.

Force from Abelian static potential Consistent with theoretical works (’ 99 Ogilvie, Faber et al. )

2 -2 Monopole dominance

Noise reduction method using random gauge transformations

Abelian, monopole and photon static potentials

Forces

String tensions Monopole dominance as well as Abelian dominance are seen very beautifully. Both are much better than in MA gauge.

3. Squeezing of electric field flux Connected correlations between NA Wilson loop and Abelian operators

Dual Meissner effect Monopoles are responsible for the dual Meissner effect.

Vacuum type Errors are still too large. We need more statistics on larger lattice.

4. Color confinement from Abelian picture

Surprizing results: 1. 2. 3. 4. Extraction of the confining component in gauge fields is possible without cooling or any gauge fixing. Gauge independence Abelian and monopole dominances are almost perfect. Squeezing of electric fields occurs due to solenoidal monopole currents. The Abelian dual Meissner effect is working. The vacuum is near the border between type 1 and 2 superconductor. Confinement of non-Abelian color charge is explained in the framework of the Abelian dual Meissner effect.