1. Gribov copy problem in lattice gauge theory simulation Bornyakov Vitaly IHEP & ITEP ICHEP0629.07.2006

2. 2 Why fixing a gauge Quark, gluon, ghost propagators Quark, gluon, ghost propagators Running coupling constant Running coupling constant Kugo-Ogima, Gribov-Zwanziger criteria Kugo-Ogima, Gribov-Zwanziger criteria of confinement of confinement Dual superconductor, center vortex Dual superconductor, center vortex theories of confinement theories of confinement Technical reasons Technical reasons

3. 3 Problems Gribov copies Gribov copies Finite volume effects for small momenta Finite volume effects for small momenta

4. 4Gauges Landau gauge Landau gauge Maximal abelian Maximal abelian gauge gauge Center gauges Center gauges

5. 5

6. 6 Two approaches to find random local minimum to find random local minimum iterative minimization iterative minimization Mandula, Ogilvie, PL B185 (1987) to find local minimum close to global to find local minimum close to global simulated annealing algorithm + simulated annealing algorithm + multiple gauge copies multiple gauge copies Bali, VB, Mueller-Preussker, Pahl, NPPS 42 (1995)

7. 7 Effects of Gribov copies Direct center gauge Direct center gauge Z2 string tension in SU(2) LGT V.B., Komarov, Polikarpov, PL B497 (2001)

8. 8 Effects of Gribov copies (contin.) Maximal Abelian gauge Maximal Abelian gauge Abelian string tension in SU(3) LGT DIK collaboration PRD 70(2001)

9. 9 Effects of Gribov copies (contin.) Landau gauge Landau gauge Ghost and gluon propagators in SU(3) Ghost and gluon propagators in SU(3) Sternbeck, Ilgenfritz, Mueller-Preussker, Schiller PR D 72 (2005) G D

10. 10 New developments Standard procedure: only periodic g. tr. New procedure: add non-periodic g. tr.

11. 11 New developments (contin.) Ghost and gluon propagators in SU(2) Ghost and gluon propagators in SU(2) Bogolubsky, Burgio, Mitryushkin, Mueller-Preussker, PRD (2006)

12. 12 New developments (contin.) Bogolubsky, VB, Burgio, Mitryushkin, Mueller-Preussker, 2006 Finite volume effects

13. 13 New developments (contin.)

14. 14 New developments (contin.) On 24^4 lattice SA is 4 times more efficient !

15. 15 Conclusions It is important to search for global minima It is important to search for global minima SA algorithm is helpful SA algorithm is helpful Non-periodic g. tr. for Landau/Coulomb Non-periodic g. tr. for Landau/Coulomb gauge – way to solve finite volume effects gauge – way to solve finite volume effects problem for small momenta problem for small momenta