Enumerating Gribov copies on the lattice

Annals of Physics

Volumn 331, Issue , 2013, Pages 188-215

  Hughes, Ciaran ^a   Mehta, Dhagash ^a,b   Skullerud, Jon Ivar ^a  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^b SYRACUSE UNIVERSITY   (United States)

Author keywords

Gauge fixing; Gribov ambiguity; Lattice gauge theory

Indexed keywords

EID: 84873244787     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2012.12.011     Document Type: Article

References (66)

1. Rothe H.J. World Sci. Lecture Notes Phys. 2005, 74:1-605.
2. Smit J. Cambridge Lect. Notes Phys. 2002, 15:1-271.
3. Montvay I., Münster G. Quantum Fields on a Lattice. Cambridge Monographs on Mathematical Physics 1994, 491. Univ. Pr., Cambridge, UK.
4. Alkofer R., von Smekal L. Phys. Rep. 2001, 353:281. arxiv://arXiv.org/abs/hep-ph/0007355.
5. Faddeev L.D., Popov V.N. Phys. Lett. B 1967, 25:29-30.
6. Becchi C., Rouet A., Stora R. Ann. Phys. 1976, 98:287-321.
7. Gribov V.N. Nuclear Phys. B 1978, 139:1.
8. Singer I.M. Comm. Math. Phys. 1978, 60:7-12.
9. Neuberger H. Phys. Lett. B 1986, 175:69.
10. Neuberger H. Phys. Lett. B 1987, 183:337.
11. Fujikawa K. Phys. Rev. Lett. 1979, 42:1195.
12. Hirschfeld P. Nuclear Phys. B 1979, 157:37.
13. Sharpe B. J. Math. Phys. 1984, 25:3324-3330.
14. L. von Smekal, D. Mehta, A. Sternbeck, A.G. Williams, Modified lattice Landau gauge, in: PoS LAT2007, 2007, p. 382. arxiv://arXiv.org/abs/0710.2410.
15. L. von Smekal, A. Jorkowski, D. Mehta, A. Sternbeck, Lattice Landau gauge via stereographic projection, in: PoS, CONFINEMENT8, 2008, p. 048. arxiv://arXiv.org/abs/0812.2992.
16. L. von Smekal, Landau gauge QCD: functional methods versus lattice simulations. arxiv://arXiv.org/abs/0812.0654.
17. Aouane R., Bornyakov V., Ilgenfritz E.-M., Mitrjushkin V., Müller-Preussker M., et al. Phys. Rev. D 2012, 85:034501. arxiv://arXiv.org/abs/1108.1735.
18. Bornyakov V., Mitrjushkin V., Rogalyov R. Phys. Rev. D 2012, 86:114503. arxiv://arXiv.org/abs/1112.4975.
19. Cucchieri A. Nuclear Phys. B 1997, 508:353-370. arxiv://arXiv.org/abs/hep-lat/9705005.
20. Holdom B. Phys. Rev. D 2008, 78:125030. arxiv://arXiv.org/abs/0712.2379.
21. Holdom B. Phys. Rev. D 2009, 79:085013. arxiv://arXiv.org/abs/0901.0497.
22. A. Ilderton, Gribov copies and confinement, eConf C0706044, 2007, p. 28. arxiv://arXiv.org/abs/0709.1671.
23. Ilderton A., Lavelle M., McMullan D. J. High Energy Phys. 2007, 0703:044. arxiv://arXiv.org/abs/hep-th/0701168.
24. Dell'Antonio G., Zwanziger D. Comm. Math. Phys. 1991, 138:291-299.
25. Schaden M. Phys. Rev. D 1999, 59:014508. arxiv://arXiv.org/abs/hep-lat/9805020.
26. Zwanziger D. Nuclear Phys. B 1989, 323:513-544.
27. Vandersickel N., Zwanziger D. Phys. Rept. 2012, 520:175-251. arxiv://arXiv.org/abs/1202.1491.
28. D. Mehta, Lattice vs. continuum: Landau gauge fixing and 't Hooft-Polyakov monopoles, Ph.D. Thesis, 2009.
29. Mehta D., Kastner M. Ann. Physics 2011, 326:1425-1440. arxiv://arXiv.org/abs/1010.5335.
30. Zwanziger D. Nuclear Phys. B 1994, 412:657-730.
31. P. van Baal, Gribov ambiguities and the fundamental domain, in: Cambridge 1997, Confinement, duality, and nonperturbative aspects of QCD, pp. 161-178. arxiv://arXiv.org/abs/hep-th/9711070.
32. Sternbeck A., Ilgenfritz E.-M., Müller-Preussker M., Schiller A. Phys. Rev. 2005, D72:014507. arxiv://arXiv.org/abs/hep-lat/0506007.
33. Catterall S., Kaplan D.B., Ũnsal M. Phys. Rept. 2009, 484:71-130. arxiv://arXiv.org/abs/0903.4881.
34. Catterall S., Galvez R., Joseph A., Mehta D. JHEP 2012, 1201:108. arxiv:1112.3588.
35. R. Galvez, S. Catterall, A. Joseph, D. Mehta, Investigating the sign problem for two-dimensional N=(2,2) and N=(8,8) lattice super Yang-Mills theories, in: PoS LATTICE2011, 2011, p. 064. arxiv://arXiv.org/abs/1201.1924.
36. D. Mehta, S. Catterall, R. Galvez, A. Joseph, Supersymmetric gauge theories on the lattice: Pfaffian phases and the Neuberger 0/0 problem, in: PoS LATTICE2011, 2011, p. 078. arxiv://arXiv.org/abs/1112.5413.
37. Parrinello C., Jona-Lasinio G. Phys. Lett. B 1990, 251:175-180.
38. Zwanziger D. Nuclear Phys. B 1990, 345:461-471.
39. Fachin S., Parrinello C. Phys. Rev. D 1991, 44:2558-2564.
40. Serreau J., Tissier M. Phys. Lett. B 2012, 712:97-103. arxiv:1202.3432.
41. Henty D., Oliveira O., Parrinello C., Ryan S. Phys. Rev. D 1996, 54:6923-6927. UKQCD Collaboration. arxiv://arXiv.org/abs/hep-lat/9607014.
42. Maas A. Phys. Lett. 2010, B689:107-111. arxiv://arXiv.org/abs/0907.5185.
43. Kalloniatis A.C., von Smekal L., Williams A.G. Phys. Lett. 2005, B609:424-429. arxiv://arXiv.org/abs/hep-lat/0501016.
44. Ghiotti M., von Smekal L., Williams A.G. AIP Conf. Proc. 2007, 892:180-182. arxiv://arXiv.org/abs/hep-th/0611058.
45. von Smekal L., Ghiotti M., Williams A.G. Phys. Rev. D 2008, 78:085016. arxiv://arXiv.org/abs/0807.0480.
46. A. Maas, Describing gauge bosons at zero and finite temperature, arxiv://arXiv.org/abs/1106.3942.
47. Hetrick J.E., dẽForcrand P., Nakamura A., Sinclair R. Nucl. Phys. Proc. Suppl. 1992, 26:432-434.
48. Private communication with Lorenz von Smekal.
49. Sommese A.J., Wampler C.W. The Numerical Solution of Systems of Polynomials Arising in Engineering and Science 2005, World Scientific Publishing Company.
50. D. Mehta, A. Sternbeck, L. von Smekal, A.G. Williams, Lattice Landau gauge and algebraic geometry, in: PoS, QCD-TNT09, 2009, p. 025. arxiv://arXiv.org/abs/0912.0450.
51. Mehta D. Phys. Rev. E 2011, 84:025702. arxiv://arXiv.org/abs/1104.5497.
52. Mehta D. Adv. High Energy Phys. 2011, 2011:263937. arxiv://arXiv.org/abs/1108.1201.
53. Kastner M., Mehta D. Phys. Rev. Lett. 2011, 107:160602. arxiv://arXiv.org/abs/1108.2345.
54. R. Nerattini, M. Kastner, D. Mehta, L. Casetti, Exploring the energy landscape of XY models, arxiv:1211.4800.
55. Mehta D., Hauenstein J.D., Kastner M. Phys. Rev. E 2012, 85:061103. arxiv://arXiv.org/abs/1202.3320.
56. Maniatis M., Mehta D. Eur. Phys. J. Plus 2012, 127:91. arxiv://arXiv.org/abs/1203.0409.
57. Mehta D., He Y.-H., Hauenstein J.D. J. High Energy Phys. 2012, 1207:018. arxiv://arXiv.org/abs/1203.4235.
58. J. Hauenstein, Y.-H. He, D. Mehta, Numerical analyses on moduli space of vacua, arxiv://arXiv.org/abs/1210.6038.
59. Li T.Y. Handbook of Numerical Analysis 2003, XI:209-304.
60. D.J. Bates, J.D. Hauenstein, A.J. Sommese, C.W. Wampler, Available at http://www.nd.edu/~sommese/bertini.
61. Verschelde J. ACM Trans. Math. Software 1999, 25(2):251-276.
62. Gunji T., Kim S., Kojima M., Takeda A., Fujisawa K., Mizutani T. Computing 2004, 73(1):57-77.
63. Gao T., Li T.Y., Wu M. ACM Trans. Math. Software 2005, 31(4):555-560.
64. Ojika T., Watanabe S., Mitsui T. J. Math. Anal. Appl. 1983, 96(2):463-479.
65. Vetterling W.T., Press W.H., Teukolsky S.A., Flannery B.P. Numerical Recipes 2007, Cambridge University Press. third ed.
66. Birmingham D., Blau M., Rakowski M., Thompson G. Phys. Rep. 1991, 209:129-340.