1. 関戸 暢 石黒克也、森祥寛、中村宜文、鈴木恒雄 Kanazawa-univ & RIKEN 共同研究者 Kanazawa-univ & RIKEN Gauge invariance of the dual Meissner effect in pure SU(2) QCD

2. Introduction Quark confinement (Y.Koma et al, KI & PRD68 (2003) 114504 and references therein, G.Bali, Talk at Confinement III, ’98 ) Quarks are confined due to the dual Meissner effect. This seems to be correct when we perform Maximally abelian (MA) projection. (‘tHooft & Mandelstam,’75) (‘tHooft,’80) Abelian magnetic currents are very important fields

3. Is the dual Meissner effect in the infrared region gauge-independent? We propose a gauge-invariant formulation following an interesting idea developed by Chernodub,Gubarev,Polikarpov and Zakharov.(2000,2002) Such beautiful results are not seen in general gauges other than some special gauges like the MA gauge. It is desirable to analyse the color confinement mechanism without performing a partial gauge-fixing such as Abelian projection.

4. NonAbelian electric fields gauge-invariant formulation Bali(1994) Phys.Rev.D51:5165-5198,1995 This is just equal to the gauge-invariant absolute value of the non-Abelian field strength itself except for the sign. Flux tube profiles was observed. Our definition of the electric fields Abelian like field strength

5. gauge-invariant formulation Abelian like field strength Gauge invariant monopole like (‘monopole’) Violation of Abelian Bianchi identity. Lorenz invariance Gauge invariance ○ ×

6. Lattice Definition Abelian like field strength Plaquette variable ‘Monopole’ definition Gauge invariant. Conserved current. Not integer.

7. Simulation details Parameters RIKEN-SX7 RCNP-SX5 These profiles are studied on a perpendicular plane at the midpoint between the two quarks. Correlation Machine We are measuring correlation between Wilson loop and various operators.

8. Result 1 Gauge invariant electric field is squeezed. φ and r components are zero. R=5,T=5

9. Result 2 Comparison with MA gauge case Magnetic solenoidal current is observed in a gauge invariant way. R=5,T=5 Correlation between Gauge invariant ‘monopole’ and Wilson loop.

10. Result 4 R=5,T=5 Abelian Bianchi identity is violated

11. Result ３ The gauge invariant ‘monopole’ width is narrower than the MA’s one. The positions of the peak of the solenoidal current distribution in gauge invariant ‘monopole’ and in MA one are near.(0.1 ～ 0.2[fm]) Comparison with MA gauge case R=5,T=5

12. Result 4 Comparison with MA gauge preliminary

13. Summary and outlook Magnetic solenoidal current is observed in a gauge invariant way. The correlation profile of gauge invariant monopole is similar to DeGrand monopole in MA gauge fixing case. The dual Meissner effect is observed in a gauge invariant way. Summary Outlook MA monopole  ‘monopole’ (gauge invariant object) Lorenz invariant and Gauge invariant definition