Center vortices as sources of abelian dominance in pure SU(2) yang-mills theory

Journal of High Energy Physics

Volumn 2008, Issue 12, 2012, Pages 1-33

  Oxman, L E ^a  

^a FLUMINENSE FEDERAL UNIVERSITY   (Brazil)

Author keywords

Confinement; Duality in gauge field theories; Solitons monopoles and instantons

Indexed keywords

EID: 85057849974     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2008/12/089     Document Type: Article

References (74)

1. Y. Nambu, Strings, monopoles and gauge fields, Phys. Rev. D 10 (1974) 4262.
2. Mandelstam, Vortices and quark confinement in nonabelian gauge theories, Phys. Rept. 23C (1976) 245.
3. G. ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B 138 (1978) 1.
4. Y.M. Cho, Extended gauge theory and its mass spectrum, Phys. Rev. D 23 (1981) 2415.
5. Y.M. Cho, Glueball spectrum in extended QCD, Phys. Rev. Lett. 46 (1981) 302;
6. Y.M. Cho, A restricted gauge theory, Phys. Rev. D 21 (1980) 1080;
7. Z.F. Ezawa and A. Iwazaki, Abelian dominance and quark confinement in Yang-Mills theories, Phys. Rev. D 25 (1982) 2681.
8. 2 vortices in SU(2) lattice gauge theory, Phys. Rev. D 55 (1997) 2298 [hep-lat/9610005].
9. L. Del Debbio, M. Faber, J. Giedt, J. Greensite and Š. Olejník, Detection of center vortices in the lattice Yang-Mills vacuum, Phys. Rev. D 58 (1998) 094501 [hep-lat/9801027].
10. P. de Forcrand and M. D’Elia, On the relevance of center vortices to QCD, Phys. Rev. Lett. 82 (1999) 4582 [hep-lat/9901020].
11. J. Greensite, The confinement problem in lattice gauge theory, Prog. Part. Nucl. Phys. 51 (2003) 1 [hep-lat/0301023].
12. M. Engelhardt, M. Quandt and H. Reinhardt, Center vortex model for the infrared sector of SU(3) Yang-Mills theory: confinement and deconfinement, Nucl. Phys. B 685 (2004) 227 [hep-lat/0311029].
13. V.N. Gribov, Quantization of non-Abelian gauge theories, Nucl. Phys. B 139 (1978) 1.
14. D. Zwanziger, Renormalizability of the critical limit of lattice gauge theory by BRS invariance, Nucl. Phys. B 399 (1993) 477.
15. R. Alkofer and L. von Smekal, The infrared behavior of QCD Green’s functions: confinement, dynamical symmetry breaking and hadrons as relativistic bound states, Phys. Rept. 353 (2001) 281 [hep-ph/0007355].
16. M.A.L. Capri, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella and R. Thibes, The gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: taking into account the effects of the Gribov copies and of the dimension two condensates, Phys. Rev. D 77 (2008) 105023 [arXiv:0801.0566].
17. A.M. Polyakov, Compact gauge fields and the infrared catastrophe, Phys. Lett. B 59 (1975) 82; Quark confinement and topology of gauge groups, Nucl. Phys. B 120 (1977) 429.
18. A.M. Polyakov, Gauge fields and strings, Contemporary concepts in physics 3, Harwood Academic Publishers, U.S.A. (1987).
19. N. Seiberg and E. Witten, Monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087].
20. G. ’t Hooft, Topology of the gauge condition and new confinement phases in nonabelian gauge theories, Nucl. Phys. B 190 (1981) 455.
21. Y.M. Cho, Abelian dominance in Wilson loops, Phys. Rev. D 62 (2000) 074009 [hep-th/9905127].
22. Y.M. Cho, H.W. Lee and D.G. Pak, Faddeev-Niemi conjecture and effective action of QCD, Phys. Lett. B 525 (2002) 347 [hep-th/0105198].
23. W.S. Bae, Y.M. Cho and S.-W. Kim, QCD versus Skyrme-Faddeev theory, Phys. Rev. D 65 (2002) 025005 [hep-th/0105163].
24. Y.M. Cho and D.G. Pak, Stable monopole-antimonopole string background in SU(2) QCD, Phys. Lett. B 632 (2006) 745 [hep-th/0510140].
25. L.D. Faddeev and A.J. Niemi, Partially dual variables in SU(2) Yang-Mills theory, Phys. Rev. Lett. 82 (1999) 1624 [hep-th/9807069].
26. S.V. Shabanov, An effective action for monopoles and knot solitons in Yang-Mills theory, Phys. Lett. B 458 (1999) 322 [hep-th/9903223].
27. M.N. Chernodub and M.I. Polikarpov, Abelian projections and monopoles, hep-th/9710205.
28. M.N. Chernodub, F.V. Gubarev, M.I. Polikarpov and A.I. Veselov, Monopoles in the Abelian projection of gluodynamics, Prog. Theor. Phys. Suppl. 131 (1998) 309 [hep-lat/9802036].
29. A. Di Giacomo, B. Lucini, L. Montesi and G. Paffuti, Colour confinement and dual superconductivity of the vacuum. I, Phys. Rev. D 61 (2000) 034503 [hep-lat/9906024].
30. A.S. Kronfeld, M.L. Laursen, G. Schierholz and U.J. Wiese, Monopole condensation and color confinement, Phys. Lett. B 198 (1987) 516.
31. Y.M. Cho, M.L. Walker and D.G. Pak, Monopole condensation and confinement of color in SU(2) QCD, JHEP 05 (2004) 073 [hep-th/0209208].
32. S. Hioki et al., Abelian dominance in SU(2) color confinement, Phys. Lett. B 272 (1991) 326 [Erratum ibid. B 281 (1992) 416].
33. T. Suzuki and I. Yotsuyanagi, A possible evidence for Abelian dominance in quark confinement, Phys. Rev. D 42 (1990) 4257;
34. D. Dudal et al., An analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge, Phys. Rev. D 70 (2004) 114038 [hep-th/0406132].
35. V.G. Bornyakov, M.N. Chernodub, F.V. Gubarev, S.M. Morozov and M.I. Polikarpov, Abelian dominance and gluon propagators in the maximally Abelian gauge of SU(2) lattice gauge theory, Phys. Lett. B 559 (2003) 214 [hep-lat/0302002].
36. D. Diakonov and V. Petrov, A formula for the Wilson loop, Phys. Lett. B 224 (1989) 131.
37. D. Diakonov and V. Petrov, Formula for a Wilson loop, Pisma Zh. Eksp. Teor. Fiz. 49 (1989) 251 [JETP Lett. 49 (1989) 284];
38. J.M. Carmona, M. D’Elia, A. Di Giacomo, B. Lucini and G. Paffuti, Color confinement and dual superconductivity of the vacuum. III, Phys. Rev. D 64 (2001) 114507 [hep-lat/0103005].
39. P. Cea and L. Cosmai, Dual superconductivity in the SU(2) pure gauge vacuum: a lattice study, Phys. Rev. D 52 (1995) 5152 [hep-lat/9504008].
40. T. Sekido, K. Ishiguro, Y. Koma, Y. Mori and T. Suzuki, Abelian dominance and the dual Meissner effect in local unitary gauges in SU(2) gluodynamics, Phys. Rev. D 76 (2007) 031501 [hep-lat/0703002].
41. J. Ambjørn, J. Giedt and J. Greensite, Vortex structure in Abelian-projected lattice gauge theory, Nucl. Phys. 83 (Proc. Suppl.) (2000) 467 [hep-lat/9908017].
42. P. de Forcrand and M. Pepe, Center vortices and monopoles without lattice Gribov copies, Nucl. Phys. B 598 (2001) 557 [hep-lat/0008016].
43. F.V. Gubarev, A.V. Kovalenko, M.I. Polikarpov, S.N. Syritsyn and V.I. Zakharov, Fine tuned vortices in lattice SU(2) gluodynamics, Phys. Lett. B 574 (2003) 136 [hep-lat/0212003].
44. T. Mendes, A. Cucchieri and A. Mihara, Infrared maximally Abelian gauge, AIP Conf. Proc. 892 (2007) 203 [hep-lat/0611002].
45. M. Engelhardt and H. Reinhardt, Center projection vortices in continuum Yang-Mills theory, Nucl. Phys. B 567 (2000) 249 [hep-th/9907139].
46. H. Reinhardt, Topology of center vortices, Nucl. Phys. B 628 (2002) 133 [hep-th/0112215].
47. K.I. Kondo, T. Murakami and T. Shinohara, BRST symmetry of SU(2) Yang-Mills theory in Cho-Faddeev-Niemi decomposition, Eur. Phys. J. C 42 (2005) 475 [hep-th/0504198].
48. M.A.L. Capri, V.E.R. Lemes, R.F. Sobreiro, S.P. Sorella and R. Thibes, A study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon, Phys. Rev. D 74 (2006) 105007 [hep-th/0609212].
49. M. Bordag, On the vacuum energy of a color magnetic vortex, Phys. Rev. D 67 (2003) 065001 [hep-th/0211080].
50. D. Diakonov and M. Maul, Center-vortex solutions of the Yang-Mills effective action in three and four dimensions, Phys. Rev. D 66 (2002) 096004 [hep-lat/0204012].
51. D. Antonov, String representation and nonperturbative properties of gauge theories, Surveys High Energy Phys. 14 (2000) 265 [hep-th/9909209].
52. K.-I. Kondo, Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum, Phys. Rev. D 74 (2006) 125003 [hep-th/0609166].
53. K.-I. Kondo, T. Shinohara and T. Murakami, Reformulating SU(N) Yang-Mills theory based on change of variables, Prog. Theor. Phys. 120 (2008) 1 [arXiv:0803.0176].
54. A.L. Leite, M. Moriconi and L.E. Oxman, How to get rid of Dirac strings and worldsheets in theories containing charged fields, to appear.
55. P.V. Buividovich, M.I. Polikarpov and V.I. Zakharov, Rigidity and percolation of center vortices, PoS(LATTICE 2007)324.
56. L.E. Oxman, String breaking and Z(2) local symmetry in the 3D Georgi-Glashow model, JHEP 08 (2004) 051 [hep-th/0403095].
57. C.D. Fosco and L.E. Oxman, Massless fermions and the instanton dipole liquid in compact QED(3), Ann. Phys. (NY) 321 (2006) 1843 [hep-th/0509145].
58. M.B. Halpern, Field strength formulation of quantum chromodynamics, Phys. Rev. D 16 (1977) 1798.
59. M. Quandt and H. Reinhardt, Field strength formulation of SU(2) Yang-Mills theory in the maximal Abelian gauge: perturbation theory, Int. J. Mod. Phys. A 13 (1998) 4049 [hep-th/9707185].
60. K.-I. Kondo, Abelian-projected effective gauge theory of QCD with asymptotic freedom and quark confinement, Prog. Theor. Phys. Suppl. 131 (1998) 243 [hep-th/9803063].
61. C.D. Fosco, V.E.R. Lemes, L.E. Oxman, S.P. Sorella and O.S. Ventura, Dual description of U(1) charged fields in (2 + 1) dimensions, Ann. Phys. (NY) 290 (2001) 27 [hep-th/0009154].
62. J. Ambjørn, Quantization of geometry, in proceedings of the Les Houches Summer School, Session 62, F. David, P. Ginsparg and J. Zinn-Justin eds., (1994) [hep-th/9411179].
63. J. Polchinski and A. Strominger, Effective string theory, Phys. Rev. Lett. 67 (1991) 1681.
64. S.-J. Rey, The Higgs mechanism for Kalb-Ramond gauge field, Phys. Rev. D 40 (1989) 3396.
65. M. Franz, Vortex-boson duality in four space-time dimensions, Europhys. Lett. 77 (2007) 47005 [cond-mat/0607310].
66. A.M. Polyakov, Confining strings, Nucl. Phys. B 486 (1997) 23 [hep-th/9607049].
67. A.M. Polyakov, String theory and quark confinement, Nucl. Phys. 68 (Proc. Suppl.) (1998) 1 [hep-th/9711002].
68. K. Bardakci and S. Samuel, Local field theory for solitons, Phys. Rev. D 18 (1978) 2849.
69. M. Kiometzis, H. Kleinert and A.M.J. Schakel, Dual description of the superconducting phase transition, Fortschr. Phys. 43 (1995) 697.
70. M.B. Halpern, A. Jevicki and P. Senjanovic, Field theories in terms of particle-string variables: spin, internal symmetries and arbitrary dimension, Phys. Rev. D 16 (1977) 2476.
71. M.B. Halpern and W. Siegel, The particle limit of field theory: a new strong coupling expansion, Phys. Rev. D 16 (1977) 2486.
72. M. Panero, A numerical study of confinement in compact QED, JHEP 05 (2005) 066 [hep-lat/0503024].
73. L.E. Oxman, Wilson loop representation for a general ensemble of monopoles and center vortices in continuum SU(2) Yang-Mills theory, to appear.
74. Y.M. Cho, Knot topology of QCD vacuum, Phys. Lett. B 644 (2007) 208 [hep-th/0409246].