Gauge independence of Abelian confinement mechansim

in SU2 gluodynamics

T. Suzuki, Kanazawa Univ., Japan(In collab. with T.Sekido, K.Ishiguro, Y.Koma)

Lattice2007-- ---31/7/2007

Surprizing results:

1. Extraction of the confining component in gauge fields is possible without cooling or any gauge fixing. Gauge independence

2. Abelian and monopole dominances are almost perfect.

3. 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.

4. 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 fluxConnected 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. Extraction of the confining component in gauge fields is possible without cooling or any gauge fixing. Gauge independence

2. Abelian and monopole dominances are almost perfect.

3. 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.

4. Confinement of non-Abelian color charge is explained in the framework of the Abelian dual Meissner effect.