Noncommutative gauge theory on fuzzy sphere from matrix model

Nuclear Physics B

Volumn 604, Issue 1-2, 2001, Pages 121-147

  Iso, Satoshi ^a,c   Kimura, Yusuke ^a,b   Tanaka, Kanji ^a,c   Wakatsuki, Kazunori ^a,d  

^a HIGH ENERGY ACCELERATOR RESEARCH ORGANIZATION KEK   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^c GRADUATE UNIVERSITY FOR ADVANCED STUDIES   (Japan)

^d TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

02.10.Sp; 02.40. k; 04.60.Nc; 04.62.+v

Indexed keywords

EID: 0000718004     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(01)00173-0     Document Type: Article

References (57)

1. Ishibashi N., Kawai H., Kitazawa Y., Tsuchiya A. A large N reduced model as superstring. Nucl. Phys. B. 498:1997;467 hep-th/9612115.
2. Banks T., Fischler W., Shenker S., Susskind L. M-theory as a matrix model: a conjecture. Phys. Rev. D. 55:1997;5112 hep-th/9610043.
3. Polchinski J. TASI Lectures on D-Branes. hep-th/9611050.
4. Taylor W. Lectures on D-branes, gauge theory and M(atrices). hep-th/9801182.
5. Eguchi T., Kawai H. Reduction of dynamical degrees of freedom in the large N gauge theory. Phys. Rev. Lett. 48:1982;1063.
6. Parisi G. A simple expression for planar field theories. Phys. Lett. B. 112:1982;463.
7. Gross D., Kitazawa Y. A quenched momentum prescription for large N theories. Nucl. Phys. B. 206:1982;440.
8. Bhanot G., Heller U., Neuberger H. The quenched Eguchi-Kawai model. Phys. Lett. B. 113:1982;47.
9. Das S., Wadia S. Translation invariance and a reduced model for summing planar diagrams in QCD. Phys. Lett. B. 117:1982;228.
10. Gonzales-Arroya A., Okawa M. The twisted Eguchi-Kawai model: a reduced model for large N lattice gauge theory. Phys. Rev. D. 27:1983;2397.
11. Aoki H., Iso S., Kawai H., Kitazawa Y., Tada T. Space-time structures from IIB matrix model. Prog. Theor. Phys. 99:1998;713 hep-th/9802085.
12. Aoki H., Iso S., Kawai H., Kitazawa Y., Tada T., Tsuchiya A. IIB matrix model. Prog. Theor. Phys. Suppl. 134:1999;47 hep-th/9908038.
13. Aoki H., Ishibashi N., Iso S., Kawai H., Kitazawa Y., Tada T. Noncommutative Yang-Mills in IIB matrix model. Nucl. Phys. B. 565:2000;176 hep-th/9908141.
14. Li M. Strings from IIB matrices. Nucl. Phys. B. 499:1997;149 hep-th/9612222.
15. Bars I., Minic D. Non-commutative geometry on a discrete periodic lattice and gauge theory. hep-th/9910091.
16. Ambjorn J., Makeenko Y.M., Nishimura J., Szabo R.J. Finite N matrix models of noncommutative gauge theory. JHEP. 9911:1999;029 hep-th/9911041.
17. Ishibashi N., Iso S., Kawai H., Kitazawa Y. Wilson loops in noncommutative Yang-Mills. Nucl. Phys. B. 573:2000;573 hep-th/9910004.
18. Kimura Y., Kitazawa Y. IIB matrix model with D1-D5 backgrounds. Nucl. Phys. B. 581:2000;295 hep-th/9912258.
19. Iso S., Kawai H., Kitazawa Y. Bi-local fields in noncommutative field theory. Nucl. Phys. B. 576:2000;375 hep-th/0001027.
20. Ishibashi N., Iso S., Kawai H., Kitazawa Y. String scale in noncommutative Yang-Mills. Nucl. Phys. B. 583:2000;159 hep-th/0004038.
21. Ambjorn J., Makeenko Y.M., Nishimura J., Szabo R.J. Lattice gauge fields and discrete noncommutative Yang-Mills theory. JHEP. 0005:2000;023 hep-th/0004147.
22. Kimura Y., Kitazawa Y. Supercurrent interactions in noncommutative Yang-Mills and IIB matrix model. Nucl. Phys. B. 598:2001;73 hep-th/0011038.
23. Seiberg N., Witten E. String theory and noncommutative geometry. JHEP. 9909:1999;032 hep-th/9908056.
24. J. Hoppe, Quantum theory of a massless relativistic surface and a two-dimensional bound state problem, MIT, Ph.D. Thesis, 1982.
25. de Wit B., Hoppe J., Nicolai H. On the quantum mechanics of supermembranes. Nucl. Phys. B. 305:1988;545.
26. Hoppe J. Diffeomorphism groups, quantization, and SU(∞) . Int. J. Mod. Phys. A. 4:1989;5235.
27. Madore J. The fuzzy sphere. Class. Quantum Grav. 9:1992;69.
28. Grosse H., Klimcik C., Presnajder P. Towards finite quantum field theory in non-commutative geometry. Int. J. Theor. Phys. 35:1996;231 hep-th/9505175.
29. Grosse H., Klimcik C., Presnajder P. Field theory on a supersymmetric lattice. Commun. Math. Phys. 185:1997;155 hep-th/9507074.
30. Grosse H., Klimcik C., Presnajder P. Topologically nontrivial field configurations in noncommutative geometry. Commun. Math. Phys. 178:1996;507 hep-th/9510083.
31. Carow-Watamura U., Watamura S. Noncommutative geometry and gauge theory on fuzzy sphere. Commun. Math. Phys. 212:2000;395 hep-th/9801195.
32. Carow-Watamura U., Watamura S. Differential calculus on fuzzy sphere and scalar field. Int. J. Mod. Phys. A. 13:1998;3235 q-alg/9710034.
33. Carow-Watamura U., Watamura S. Chirality and dirac operator on noncommutative sphere. Commun. Math. Phys. 183:1997;365 hep-th/9605003.
34. Klimcik C. Gauge theories on the noncommutative sphere. Commun. Math. Phys. 199:1998;257 hep-th/9710153.
35. Grosse H., Madore J. A noncommutative version of the Schwinger model. Phys. Lett. B. 283:1992;218.
36. Grosse H., Presnajder P. The Dirac operators on the fuzzy sphere. Lett. Math. Phys. 33:1995;171.
37. Baez S., Balachandran A.P., Vaidya S., Ydri B. Monopoles and solitons in fuzzy physics. Commun. Math. Phys. 208:2000;787 hep-th/9811169.
38. Balachandran A.P., Vaidya S. Instantons and chiral anomaly in fuzzy physics. hep-th/9910129.
39. Balachandran A.P., Govindarajan T.R., Ydri B. The fermion doubling problem and noncommutative geometry. Mod. Phys. Lett. A. 15:2000;1279 hep-th/9911087.
40. Balachandran A.P., Martin X., O'Connor D. Fuzzy actions and their continuum limits. hep-th/0007030.
41. Klimcik C. A nonperturbative regularization of the supersymmetric Schwinger model. Commun. Math. Phys. 206:1999;567 hep-th/9903112.
42. Kabat D., Taylor W. Spherical membranes in matrix theory. Adv. Theor. Math. Phys. 2:1998;181 hep-th/9711078.
43. Rey S.-J. Gravitating M(atrix) Q-balls. hep-th/9711081.
44. Myers R.C. Dielectric branes. JHEP. 9912:1999;022 hep-th/9910053.
45. Alekseev A.Yu., Recknagel A., Schomerus V. Non-commutative world-volume geometries: branes on SU(2) and fuzzy spheres. JHEP. 9909:1999;023 hep-th/9908040.
46. Alekseev A.Yu., Recknagel A., Schomerus V. Brane dynamics in background fluxes and non-commutative geometry. JHEP. 0005:2000;010 hep-th/0003187.
47. 2 . Helv. Phys. Acta. 61:1988;636.
48. Krauth W., Staudacher M. Finite Yang-Mills integrals. Phys. Lett. B. 435:1998;350 hep-th/9804199.
49. Krauth W., Staudacher M. Eigenvalue distributions in Yang-Mills integrals. Phys. Lett. B. 453:1999;253 hep-th/9902113.
50. Hashimoto K., Krasnov K. D-brane solutions in non-commutative gauge theory on fuzzy sphere. hep-th/0101145.
51. Berezin F.A. General concept of quantization. Commun. Math. Phys. 40:1975;153.
52. Man'ko V.I., Marmo G., Sudarshan E.C.G., Zaccaria F. Wigner's problem and alternative commutation relations for quantum mechanics. quant-ph/9612007.
53. Alexanian G., Pinzul A., Stern A. Generalized coherent state approach to star products and applications to the fuzzy sphere. hep-th/0010187.
54. Saito S., Wakatsuki K. Symmetrization of Berezin star product and path-integral quantization. Prog. Theor. Phys. 104:2000;893 hep-th/9912265.
55. Wakatsuki K. Symmetrization of Berezin quantization. hep-th/0006096.
56. Masuda T. Normalized Weyl-type -product on Kähler manifolds. Mod. Phys. Lett. A. 15:2000;2177 hep-th/0010009.
57. Holstein T., Primakoff H. Field dependence of the intrinsic domain magnetization of ferromagnet. Phys. Rev. 58:1940;1098.