Open Wilson lines and group theory of noncommutative Yang-Mills theory in two dimensions

Journal of High Energy Physics

Volumn 7, Issue 5, 2003, Pages 625-659

  Paniak, Lori D ^a   Szabo, Richard J ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Non Commutative Geometry; Nonperturbative Effects; Strong Coupling Expansion

Indexed keywords

EID: 21444457327     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2003/05/029     Document Type: Article

References (43)

1. A. Konechny and A. Schwarz, Introduction to M(atrix) theory and noncommutative geometry, Phys. Rept. 360 (2002) 353 [hep-th/0012145];
2. Introduction to M(atrix) theory and noncommutative geometry, II, Phys. Rept. 360 (2002) 353 [hep-th/0107251].
3. M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048].
4. R. J. Szabo, Quantum field theory on noncommutative spaces, Phys. Rept. 378 (2003) 207 [hep-th/0109162].
5. S. Cordes, G.W. Moore and S. Ramgoolam, Lectures on 2-d Yang-Mills theory, equivariant cohomology and topological field theories, Nucl. Phys. 41 (Proc. Suppl.) (1995) 184 [hep-th/9411210].
6. A. Bassetto, G. Nardelli and A. Torrielli, Perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory, Nucl. Phys. B 617 (2001) 308 [hep-th/0107147].
7. A. Bassetto, G. Nardelli and A. Torrielli, Scaling properties of the perturbative wilson loop in two-dimensional non-commutative Yang-Mills theory, Phys. Rev. D 66 (2002) 085012 [hep-th/0205210].
8. A. Torrielli, Noncommutative perturbative quantum field theory: Wilson loop in two-dimensional Yang-Mills and unitarity from string theory, hep-th/0301091.
9. 2: Morita equivalence and large-N-limit, J. High Energy Phys. 12 (2001) 024 [hep-th/0110293].
10. A. Bassetto and F. Vian, Wilson line correlators in two-dimensional noncommutative Yang-Mills theory, J. High Energy Phys. 10 (2002) 004 [hep-th/0207222].
11. W. Bietenholz, F. Hofheinz and J. Nishimura, The renormalizability of 2d Yang-Mills theory on a non-commutative geometry, J. High Energy Phys. 09 (2002) 009 [hep-th/0203151].
12. W. Bietenholz, F. Hofheinz and J. Nishimura, Simulating non-commutative field theory, hep-lat/0209021.
13. W. Bietenholz, F. Hofheinz and J. Nishimura, Non-commutative field theories beyond perturbation theory, hep-th/0212258.
14. L.D. Paniak and R. J. Szabo, Instanton expansion of noncommutative gauge theory in two dimensions, hep-th/0203166.
15. M.M. Sheikh-Jabbari, Open strings in a B-field background as electric dipoles, Phys. Lett. B 455 (1999) 129 [hep-th/9901080].
16. D. Bigatti and L. Susskind, Magnetic fields, branes and noncommutative geometry, Phys. Rev. D 62 (2000) 066004 [hep-th/9908056].
17. M.R. Douglas, K. Li and M. Staudacher, Generalized two-dimensional QCD, Nucl. Phys. B 420 (1994) 118 [hep-th/9401062].
18. O. Ganor, J. Sonnenschein and S. Yankielowicz, The string theory approach to generalized 2-d Yang-Mills theory, Nucl. Phys. B 434 (1995) 139 [hep-th/9407114].
19. B. Rusakov and S. Yankielowicz, Large-N phase transitions and multicritical behavior in generalized 2-d QCD, Phys. Lett. B 339 (1994) 258 [hep-th/9408046].
20. D.J. Gross, A. Hashimoto and N. Itzhaki, Observables of non-commutative gauge theories, Adv. Theor. Math. Phys. 4 (2000) 893 [hep-th/0008075].
21. M. Rozali and M. Van Raamsdonk, Gauge invariant correlators in non-commutative gauge theory, Nucl. Phys. B 608 (2001) 103 [hep-th/0012065].
22. A. Dhar and Y. Kitazawa, High energy behavior of Wilson lines, J. High Energy Phys. 02 (2001) 004 [hep-th/0012170].
23. M.R. Douglas and V.A. Kazakov, Large-N phase transition in continuum QCD in two-dimensions, Phys. Lett. B 319 (1993) 219 [hep-th/9305047].
24. B.E. Rusakov, Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds, Mod. Phys. Lett. A 5 (1990) 693.
25. A.M. Polyakov, Thermal properties of gauge fields and quark liberation, Phys. Lett. B 72 (1978) 477.
26. L. Susskind, Lattice models of quark confinement at high temperature, Phys. Rev. D 20 (1979) 2610.
27. L.D. Paniak, Order parameter for confinement in large-N gauge theories with fundamental matter, Phys. Rev. D 56 (1997) 6566 [hep-th/9707092].
28. G. Grignani, L. Paniak, G.W. Semenoff and P. Sodano, Loop correlators and theta states in two-dimensional Yang-Mills theory, Ann. Phys. (NY) 260 (1997) 275 [hep-th/9705102].
29. J. Ambjørn, Y.M. Makeenko, J. Nishimura and R. J. Szabo, Lattice gauge fields and discrete noncommutative Yang-Mills theory, J. High Energy Phys. 05 (2000) 023 [hep-th/0004147].
30. Z. Guralnik and J. Troost, Aspects of gauge theory on commutative and noncommutative tori, J. High Energy Phys. 05 (2001) 022 [hep-th/0103168].
31. C. Hofman and E. Verlinde, Gauge bundles and Born-Infeld on the noncommutative torus, Nucl. Phys. B 547 (1999) 157 [hep-th/9810219].
32. A. Konechny and A. Schwarz, Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori, Phys. Lett. B 453 (1999) 23 [hep-th/9901077].
33. N. Ishibashi, S. Iso, H. Kawai and Y. Kitazawa, Wilson loops in noncommutative Yang-Mills, Nucl. Phys. B 573 (2000) 573 [hep-th/9910004].
34. S.-J. Rey and R. von Unge, S-duality, noncritical open string and noncommutative gauge theory, Phys. Lett. B 499 (2001) 215 [hep-th/0007089].
35. S.R. Das and S.-J. Rey, Open wibon lines in noncommutative gauge theory and tomography of holographic dual supergravity, Nucl. Phys. B 590 (2000) 453 [hep-th/0008042].
36. A. Konechny and A. Schwarz, 1/4-BPS states on noncommutative tori, J. High Energy Phys. 09 (1999) 030 [hep-th/9907008].
37. N.A. Obers and B. Pioline, U-duality and M-theory, Phys. Rept. 318 (1999) 113 [hep-th/9809039].
38. E. Witten, Two-dimensional gauge theories revisited, J. Geom. Phys. 9 (1992) 303 [hep-th/9204083].
39. E. Langmann and R.J. Szabo, Teleparallel gravity and dimensional reductions of noncommutative gauge theory, Phys. Rev. D 64 (2001) 104019 [hep-th/0105094].
40. Y. Kiem, S.-J. Rey, H.-T. Sato and J.-T. Yee, Open Wilson lines and generalized star product in nocommutative scalar field theories, Phys. Rev. D 65 (2002) 026002 [hep-th/0106121].
41. Y. Kiem, S. Lee, S.-J. Rey and H.-T. Sato, Interacting open Wilson lines in noncommutative field theories, Phys. Rev. D 65 (2002) 046003 [hep-th/0110215].
42. S.-J. Rey, Exact answers to approximate questions: noncommutative dipoles, open Wilson lines and UV-IR duality, hep-th/0207108.
43. Z. Guralnik, R.C. Helling, K. Landsteiner and E. Lopez, Perturbative instabilities on the non-commutative torus, morita duality and twisted boundary conditions, J. High Energy Phys. 05 (2002) 025 [hep-th/0204037].