Large N reduction with the Twisted Eguchi-Kawai model

Journal of High Energy Physics

Volumn 2010, Issue 7, 2010, Pages

  González Arroyoa, Antonio ^a   Okawab, Masanori ^b  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b HIROSHIMA UNIVERSITY   (Japan)

Author keywords

1 N expansion; Lattice gauge field theories; Matrix models

Indexed keywords

EID: 77954996393     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP07(2010)043     Document Type: Article

References (34)

1. T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large-N gauge theory, Phys. Rev. Lett. 48 (1982) 1063.
2. Y. M. Makeenko and A. A. Migdal, Exact equation for the loop average in multicolor QCD, Phys. Lett. B 88 (1979) 135
3. [Erratum ibid. B 89 (1980) 437].
4. G. Bhanot, U. M. Heller and H. Neuberger, The quenched Eguchi-Kawai model, Phys. Lett. B 113 (1982) 47.
5. A. Gonzalez-Arroyo and M. Okawa, A twisted model for large-N lattice gauge theory, Phys. Lett. B 120 (1983) 174.
6. A. Gonzalez-Arroyo and M. Okawa, Twisted Eguchi-Kawai model: a reduced model for large-N lattice gauge theory, Phys. Rev. D 27 (1983) 2397.
7. S. R. Das, Some aspects of large-N theories, Rev. Mod. Phys. 59 (1987) 235.
8. A. Gonzalez-Arroyo and C. P. Korthals Altes, Reduced model for large-N continuum field theories, Phys. Lett. B 131 (1983) 396.
9. M. R. Douglas and N. A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048].
10. J. Ambjørn, Y. M. Makeenko, J. Nishimura and R. J. Szabo, Finite N matrix models of noncommutative gauge theory, JHEP 11 (1999) 029 [hep-th/9911041].
11. J. Ambjørn, Y. M. Makeenko, J. Nishimura and R. J. Szabo, Nonperturbative dynamics of noncommutative gauge theory, Phys. Lett. B 480 (2000) 399 [hep-th/0002158].
12. J. Ambjørn, Y. M. Makeenko, J. Nishimura and R. J. Szabo, Lattice gauge fields and discrete noncommutative Yang-Mills theory, JHEP 05 (2000) 023 [hep-th/0004147].
13. N symmetry breaking on the numerical simulation of twisted Eguchi-Kawai model, talk given at the Annual Meeting of the Physical Society of Japan, March 28-31, Sendai, Japan (2003).
14. M. Teper and H. Vairinhos, Symmetry breaking in twisted Eguchi-Kawai models, Phys. Lett. B 652 (2007) 359 [hep-th/0612097].
15. H. Vairinhos and M. Teper, Structure and properties of the vacuum of the Twisted Eguchi-Kawai model, PoS (LATTICE 2007) 282 [arXiv:0710.3337].
16. T. Azeyanagi, M. Hanada, T. Hirata and T. Ishikawa, Phase structure of twisted Eguchi-Kawai model, JHEP 01 (2008) 025 [arXiv:0711.1925].
17. T. Ishikawa, T. Azeyanagi, M. Hanada and T. Hirata, Phase structure of twisted Eguchi-Kawai model, PoS (LATTICE 2007) 054 [arXiv:0710.2919].
18. B. Bringoltz and S. R. Sharpe, Breakdown of large-N quenched reduction in SU (N) lattice gauge theories, Phys. Rev. D 78 (2008) 034507 [arXiv:0805.2146].
19. P. Kovtun, M. Ünsal and L. G. Yaffe, Volume independence in large-Nc QCD-like gauge theories, JHEP 06 (2007) 019 [hep-th/0702021].
20. R. Narayanan and H. Neuberger, Large-N reduction in continuum, Phys. Rev. Lett. 91 (2003) 081601 [hep-lat/0303023].
21. G. Aldazabal, N. Parga, M. Okawa and A. Gonzalez-Arroyo, Large-N reduced models and stochastic quantization, Phys. Lett. B 129 (1983) 90.
22. P. van Baal, Surviving extrema for the action on the twisted SU (∞) one point lattice, Commun. Math. Phys. 92 (1983) 1.
23. A. Gonzalez-Arroyo, J. Jurkiewicz and C. P. Korthals-Altes, Ground state metamorphosis for Yang-Mills fields on a finite periodic lattice, talk given at Freiburg NATO Summer Inst., September 30-October 10, Freiburg, Germany (1981).
24. A. Coste, A. Gonzalez-Arroyo, J. Jurkiewicz and C. P. Korthals Altes, Zero momentum contribution to Wilson loops in periodic boxes, Nucl. Phys. B 262 (1985) 67.
25. M. Garcia Perez, A. Gonzalez-Arroyo and M. Okawa, Weak coupling behaviour of the twisted Eguchi-Kawai model, work in progress.
26. K. Fabricius and O. Haan, Heat bath method for the twisted Eguchi-Kawai model, Phys. Lett. B 143 (1984) 459.
27. B. Lucini, M. Teper and U. Wenger, Properties of the deconfining phase transition in SU (N) gauge theories, JHEP 02 (2005) 033 [hep-lat/0502003].
28. A. Gonzalez-Arroyo and M. Okawa, String tension for large-N gauge theory, Phys. Lett. B 133 (1983) 415.
29. J. Kiskis and R. Narayanan, Computation of the string tension in four-dimensional Yang-Mills theory using large-N reduction, Phys. Lett. B 681 (2009) 372 [arXiv:0908.1451].
30. R. Narayanan and H. Neuberger, Infinite N phase transitions in continuum Wilson loop operators, JHEP 03 (2006) 064 [hep-th/0601210].
31. A. Gonzalez-Arroyo and A. Montero, Do classical configurations produce Confinement?, Phys. Lett. B 387 (1996) 823 [hep-th/9604017].
32. M. Lüscher, K. Symanzik and P. Weisz, Anomalies of the free loop wave equation in the WKB approximation, Nucl. Phys. B 173 (1980) 365.
33. Z. Guralnik, R. C. Helling, K. Landsteiner and E. Lopez, Perturbative instabilities on the non-commutative torus, Morita duality and twisted boundary conditions, JHEP 05 (2002) 025 [hep-th/0204037].
34. W. Bietenholz, J. Nishimura, Y. Susaki and J. Volkholz, A non-perturbative study of 4D U (1) non-commutative gauge theory: the fate of one-loop instability, JHEP 10 (2006) 042 [hep-th/0608072].