Monte Carlo simulation of a NC gauge theory on the fuzzy sphere

Journal of High Energy Physics

Volumn 2006, Issue 11, 2006, Pages

  O'Connor, Denjoe ^a   Ydri, Badis ^b  

^a DUBLIN INSTITUTE FOR ADVANCED STUDIES   (Ireland)

^b BADJI MOKHTAR UNIVERSITY   (Algeria)

Author keywords

Gauge Symmetry; Matrix Models; Non Commutative Geometry; Nonperturbative Effects

Indexed keywords

EID: 33846231465     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2006/11/016     Document Type: Review

References (72)

1. R.J. Szabo, Quantum field theory on noncommutative spaces 2003 Phys. Rep. 378 207 [hep-th/0109162]
2. C.P. Martin and F. Ruiz Ruiz, Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1) 2001 Nucl. Phys. B 597 197 [hep-th/0007131]
3. For a treatement of the same problem on the 4D NC torus see: T. Krajewski and R. Wulkenhaar, Perturbative quantum gauge fields on the noncommutative torus 2000 Int. J. Mod. Phys. A 15 1011 [hep-th/9903187]
4. 4, [hep-th/9912167]
5. S. Minwalla, M. Van Raamsdonk and N. Seiberg, Noncommutative perturbative dynamics 2000 J. High Energy Phys. JHEP02(2000)020 [hep-th/9912072]
6. M.R. Douglas and N.A. Nekrasov, Noncommutative field theory 2001 Rev. Mod. Phys. 73 977 [hep-th/0106048]
7. 4. This phase was predicted on the fuzzy sphere originally (theoretically and numerically) in [15] and [16] (respectively)
8. S.S. Gubser and S.L. Sondhi, Phase structure of non-commutative scalar field theories 2001 Nucl. Phys. B 605 395 [hep-th/0006119]
9. J. Ambjørn and S. Catterall, Stripes from (noncommutative) stars 2002 Phys. Lett. B 549 253 [hep-lat/0209106]
10. 4 model in D = 3 2004 J. High Energy Phys. JHEP06(2004)042 [hep-th/0404020]
11. W. Bietenholz, F. Hofheinz and J. Nishimura, Nucl. Phys. (Proc. Suppl.) 119 941
12. B. Ydri, Fuzzy physics [hep-th/0110006]
13. H. Grosse, C. Klimcik, P. Presnajder, 1996 Commun. Math. Phys. 180 429
14. H. Grosse, C. Klimcik, P. Pre snajder, Towards finite quantum field theory in noncommutative geometry 1996 Int. J. Theor. Phys. 35 231 [hep-th/9505175]
15. D. O'Connor, Field theory on low dimensional fuzzy spaces 2003 Mod. Phys. Lett. A 18 2423
16. C.Klimcik, Commun. Math. Phys. 199 (1998) 257
17. J. Madore, The fuzzy sphere 1992 Class. Quantum Grav. 9 69
18. J.Hoppe, MIT PhD thesis, 1982
19. J.Hoppe, S.T.Yau, Commun. Math. Phys. 195 (1998) 67
20. A.Y. Alekseev, A. Recknagel and V. Schomerus, Brane dynamics in background fluxes and non-commutative geometry 2000 J. High Energy Phys. JHEP05(2000)010 [hep-th/0003187]
21. A.Y. Alekseev and V. Schomerus, D-branes in the WZW model 1999 Phys. Rev. D 60 061901 [hep-th/9812193]
22. S. Iso, Y. Kimura, K. Tanaka and K. Wakatsuki, Noncommutative gauge theory on fuzzy sphere from matrix model 2001 Nucl. Phys. B 604 121 [hep-th/0101102]
23. X.Martin, 2004 J. High Energy Phys. JHEP04(2004)77; Simulating the scalar field using the fuzzy sphere 2003 Mod. Phys. Lett. A 18 2389
24. F. Garcia Flores, D. O'Connor and X. Martin, Simulating the scalar field on the fuzzy sphere 2006 PoS LAT2005 262 [hep-lat/0601012]
25. J. Medina, W. Bietenholz, F. Hofheinz and D. O'Connor, Field theory simulations on a fuzzy sphere: an alternative to the lattice 2006 PoS LAT2005 263 [hep-lat/0509162]
26. B. Ydri, The one-plaquette model limit of NC gauge theory in 2D [hep-th/0606206]
27. 2 2001 Phys. Lett. B 512 403 [hep-th/0102212]
28. 4 models on the fuzzy sphere and their continuum limits 2002 J. High Energy Phys. JHEP03(2002)013 [hep-th/0109084]
29. B.P. Dolan, D. O'Connor and P. Presnajder, Fuzzy complex quadrics and spheres 2004 J. High Energy Phys. JHEP02(2004)055 [hep-th/0312190]
30. T. Imai, Y. Kitazawa, Y. Takayama and D. Tomino, Quantum corrections on fuzzy sphere 2003 Nucl. Phys. B 665 520 [hep-th/0303120]
31. S. Vaidya and B. Ydri, New scaling limit for fuzzy spheres [hep-th/0209131]
32. C.S.Chu, J.Madore, H.Steinacker, 2001 J. High Energy Phys. JHEP08(2001)38
33. 4 models on the fuzzy sphere and their continuum limits 2002 J. High Energy Phys. JHEP03(2002)013 [hep-th/0109084]
34. 2 2005 J. High Energy Phys. JHEP09(2005)066 [hep-th/0506044]
35. 4, 2005 J. High Energy Phys. JHEP07(2005)040 [hep-th/0503041]
36. 2 geometry in IIB matrix model 2004 Nucl. Phys. B 686 248 [hep-th/0312241]
37. 2 2005 J. High Energy Phys. JHEP09(2005)047 [hep-th/0506205]
38. 4 phase in the dimensionally reduced 5D Yang-Mills-Chern-Simons model 2004 J. High Energy Phys. JHEP07(2004)066 [hep-th/0405096]
39. H. Steinacker, A non-perturbative approach to non-commutative scalar field theory 2005 J. High Energy Phys. JHEP03(2005)075 [hep-th/0501174]
40. 2 in the large-N reduced model with a cubic term 2006 J. High Energy Phys. JHEP05(2006)061 [hep-th/0405277]
41. Badis Ydri, 2004 Mod.Phys.Lett. A 19 2205; Exact solution of noncommutative U(1) gauge theory in 4-dimensions 2004 Nucl. Phys. B 690 230 [hep-th/0403233]
42. G.Alexanian, A.P.Balachandran, G.Immirzi, B.Ydri, 2002 J.Geo.Phys. 42 28-53
43. H. Grosse and A. Strohmaier, Noncommutative geometry and the regularization problem of 4d quantum field theory 1999 Lett. Math. Phys. 48 163 [hep-th/9902138]
44. 2 2005 Nucl. Phys. B 707 145 [hep-th/0407089]
45. J.Medina,D.O'Connor, 2003 J. High Energy Phys. JHEP11(2003)051
46. Y.Kimura, 2002 Nucl. Phys. B 637 177
47. T. Eguchi and H. Kawai, Reduction of dynamical degrees of freedom in the large-N gauge theory 1982 Phys. Rev. Lett. 48 1063
48. J. Ambjørn, Y.M. Makeenko, J. Nishimura and R.J. Szabo, Lattice gauge fields and discrete noncommutative Yang-Mills theory 2000 J. High Energy Phys. JHEP05(2000)023 [hep-th/0004147]
49. P. Castro-Villarreal, R. Delgadillo-Blando and B. Ydri, A gauge-invariant UV-IR mixing and the corresponding phase transition for U(1) fields on the fuzzy sphere 2005 Nucl. Phys. B 704 111 [hep-th/0405201]
50. T. Azuma, S. Bal, K. Nagao and J. Nishimura, Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term 2004 J. High Energy Phys. JHEP05(2004)005 [hep-th/0401038]
51. H. Steinacker, Quantized gauge theory on the fuzzy sphere as random matrix model 2004 Nucl. Phys. B 679 66 [hep-th/0307075]
52. D.J. Gross and E. Witten, Possible third order phase transition in the large-N lattice gauge theory 1980 Phys. Rev. D 21 446
53. See also S.R. Wadia, EFI preprint EFI 80/15 March 1980
54. See also S.R. Wadia, N = ∞ phase transition in a class of exactly soluble model lattice gauge theories 1980 Phys. Lett. B 93 403
55. S. Baez, A.P. Balachandran, S. Vaidya, B. Ydri, 2000 Commun. Math. Phys. 208 787
56. A.P. Balachandran, S. Vaidya, 2001 Mod. Phys. A 16 17
57. H.Grosse, C.Klimcik, P.Presnajder, 1996 Commun. Math. Phys. 178 507
58. H.Grosse, C.W.Rupp, A.Strohmaier, J. Geom. Phys. 42 (2002) 54-63
59. H. Aoki, S. Iso and K. Nagao, Ginsparg-Wilson relation and 't Hooft-Polyakov monopole on fuzzy 2-sphere 2004 Nucl. Phys. B 684 162 [hep-th/0312199]
60. A.P. Balachandran, T.R. Govindarajan and B. Ydri, The fermion doubling problem and noncommutative geometry, II [hep-th/0006216]
61. H. Aoki, S. Iso and K. Nagao, Ginsparg-Wilson relation, topological invariants and finite noncommutative geometry 2003 Phys. Rev. D 67 085005 [hep-th/0209223]
62. A.P. Balachandran and G. Immirzi, The fuzzy ginsparg-wilson algebra: a solution of the fermion doubling problem 2003 Phys. Rev. D 68 065023 [hep-th/0301242]
63. 2003 Int. J. Mod. Phys. A 18 5981
64. U. Carow-Watamura, S. Watamura, 1997 Commun. Math. Phys. 183 365-382; Differential calculus on fuzzy sphere and scalar field 1998 Int. J. Mod. Phys. A 13 3235 [q-alg/9710034]
65. B. Ydri, Noncommutative chiral anomaly and the Dirac-Ginsparg-Wilson operator 2003 J. High Energy Phys. JHEP08(2003)046 [hep-th/0211209]
66. H. Aoki, S. Iso and K. Nagao, Chiral anomaly on fuzzy 2-sphere 2003 Phys. Rev. D 67 065018 [hep-th/0209137]
67. H. Grosse and P. Presnajder, A treatment of the schwinger model within noncommutative geometry [hep-th/9805085]
68. A.P. Balachandran, S. Kurkcuoglu and S. Vaidya, Lectures on fuzzy and fuzzy SUSY physics [hep-th/0511114]
69. K.N. Anagnostopoulos, T. Azuma, K. Nagao and J. Nishimura, Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres 2005 J. High Energy Phys. JHEP09(2005)046 [hep-th/0506062]
70. J. Volkholz, W. Bietenholz, J. Nishimura and Y. Susaki, PoS, LAT2005 (2006) 264
71. W. Bietenholz et al., Numerical results for U(1) gauge theory on 2D and 4D non-commutative spaces 2005 Fortschr. Phys. 53 418 [hep-th/0501147]
72. W. Bietenholz, F. Hofheinz, J. Nishimura, Y. Susaki and J. Volkholz, First simulation results for the photon in a non-commutative space 2005 Nucl. Phys. (Proc. Suppl.) 140 772 [hep-lat/0409059]