Zero modes and the Atiyah-Singer index in noncommutative instantons

Physical Review D

Volumn 66, Issue 2, 2002, Pages

  Kim, Keun Young ^a   Lee, Bum Hoon ^a   Yang, Hyun Seok ^b  

^a Sogang University   (South Korea)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ATOMIC PARTICLE; CHIRALITY; MATHEMATICAL MODEL; QUANTUM THEORY; SPACE;

EID: 0037101261     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.66.025034     Document Type: Article

References (72)

1. A.A. Belavin, A.M. Polyakov, A.S. Schwartz, and Yu.S. Tyupkin, Phys. Lett. 59B, 85 (1975).
2. R. Jackiew and C. Rebbi, Phys. Rev. Lett. 37, 172 (1976).
3. C.G. Callan, R.F. Dashen, and D.J. Gross, Phys. Lett. 63B, 334 (1976).
4. Instantons in Gauge Theories, edited by M. Shifman (World Scientific, Singapore, 1994).
5. G. 't Hooft, Phys. Rev. Lett. 37, 8 (1976).
6. G. 't Hooft, Phys. Rev. D 14, 3432 (1976);
7. G. 't Hooft, Phys. Rev. D 18, 2199(E) (1978).
8. For a recent review, for example, see T. Schafer and E.V. Shuryak, Rev. Mod. Phys. 70, 323 (1998).
9. E. Witten, Nucl. Phys. B460, 541 (1996).
10. M.R. Douglas, "Branes within branes," hep-th/9512077;
11. J. Geom. Phys. 28, 255 (1998).
12. A. Strominger and C. Vafa, Phys. Lett. B 379, 99 (1996).
13. C.G. Callan and J.M. Maldacena, Nucl. Phys. B472, 591 (1996).
14. T. Banks and M.B. Green, J. High Energy Phys. 05, 002 (1998).
15. M. Bianchi, M.B. Green, S. Kovacs, and G. Rossi, J. High Energy Phys. 08, 013 (1998).
16. N. Dorey, T.J. Hollowood, V.V. Khoze, M.P. Mattis, and S. Vandoren, Nucl. Phys. B552, 88 (1999).
17. For a review on Yang-Mills and D-instantons, see A.V. Belitsky, S. Vandoren, and P. van Nieuwenhuizen, Class. Quantum Grav. 17, 3521 (2000).
18. N.A. Nekrasov and A. Schwarz, Commun. Math. Phys. 198, 689 (1998).
19. N. Seiberg and E. Witten, J. High Energy Phys. 09, 032 (1999).
20. M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, and Yu.I. Manin, Phys. Lett. 65A, 185 (1978).
21. K. Lee and P. Yi, Phys. Rev. D 61, 125015 (2000).
22. H.W. Braden and N.A. Nekrasov, "Spacetime foam from non-commutative instantons," hep-th/9912019.
23. K. Furuuchi, Prog. Theor. Phys. 103, 1041 (2000).
24. A. Kapustin, A. Kuznetsov, and D. Orlov, Commun. Math. Phys. 221, 385 (2001).
25. P.-M. Ho, "Twisted bundle on noncommuative space and U(1) instanton," hep-th/0003012.
26. 4," hep-th/0003093.
27. K. Furuuchi, Commun. Math. Phys. 217, 579 (2001).
28. K. Lee, D. Tong, and S. Yi, Phys. Rev. D 63, 065017 (2001).
29. K. Furuuchi, J. High Energy Phys. 03, 223 (2001).
30. A. Schwarz, Commun. Math. Phys. 221, 433 (2001).
31. D.H. Correa, G.S. Lozano, E.F. Moreno, and F.A. Schaposnik, Phys. Lett. B 515, 206 (2001).
32. C.-S. Chu, V.V. Khoze, and G. Travaglini, Nucl. Phys. B621, 101 (2002).
33. M. Hamanaka, Phys. Rev. D 65, 085022 (2002).
34. T. Ishikawa, S.-I. Kuroki, and A. Sako, J. High Energy Phys. 11, 068 (2001).
35. K.-Y. Kim, B.-H. Lee, and H.S. Yang, Phys. Lett. B 523, 357 (2001).
36. O. Lechtenfeld and A.D. Popov, J. High Energy Phys. 03, 040 (2002).
37. 4," hep-th/0201196.
38. N. Dorey, T.J. Hollowood, and V.V. Khoze, J. High Energy Phys. 03, 040 (2001).
39. T.J. Hollowood, V.V. Khoze, and G. Travaglini, J. High Energy Phys. 05, 051 (2001).
40. N. Dorey, T.J. Hollowood, and V.V. Khoze, "Notes on soliton bound-state problems in gauge theory and string theory," hep-th/0105090.
41. C. Kim, K. Lee, and P. Yi, Phys. Rev. D 65, 065024 (2002).
42. T.J. Hollowood, J. High Energy Phys. 03, 038 (2002).
43. N.A. Nekrasov, "Lectures on open strings and noncommutative gauge theories," hep-th/0203109.
44. C.W. Bernard, N.H. Christ, A.H. Guth, and E.J. Weinberg, Phys. Rev. D 16, 2967 (1977).
45. E.F. Corrigan, D.B. Fairlie, P. Goddard, and S. Templeton, Nucl. Phys. B140, 31 (1978).
46. H. Osborn, Nucl. Phys. B140, 45 (1978).
47. N.H. Christ, N.K. Stanton, and E.J. Weinberg, Phys. Rev. D 18, 2013 (1978).
48. E.F. Corrigan, P. Goddard, and S. Templeton, Nucl. Phys. B151, 93 (1979).
49. E. Corrigan and P. Goddard, Ann. Phys. (N.Y.) 154, 253 (1984).
50. R. Jackiew, C. Nohl, and C. Rebbi, Phys. Rev. D 15, 1642 (1977).
51. E. Corrigan, P. Goddard, H. Osborn, and S. Templeton, Nucl. Phys. B159, 469 (1979).
52. P. Mansfield, Nucl. Phys. B186, 287 (1981).
53. H. Osborn, Ann. Phys. (N.Y.) 135, 373 (1981).
54. R. Jackiew and C. Rebbi, Phys. Rev. D 16, 1052 (1977).
55. H. Nakajima, Ann. Math. 145, 379 (1997);
56. Lectures on Hilbert Schemes of Points on Surfaces (American Mathematical Society, Providence, 1999).
57. M. Aganagic, R. Gopakumer, S. Minwalla, and A. Stronminger, J. High Energy Phys. 04, 001 (2001).
58. J.A. Harvey, P. Kraus, and F. Larsen, J. High Energy Phys. 12, 024 (2000).
59. K. Hashimoto and H. Ooguri, Phys. Rev. D 64, 106005 (2001).
60. R. Gopakumar, S. Minwalla, and A. Strominger, J. High Energy Phys. 05, 020 (2000).
61. C.-T. Chan, C.-M. Chen, L.-F. Li, and H.S. Yang, Nucl. Phys. B625, 327 (2002).
62. V.A. Novikov, M.A. Shifman, A.I. Vainstein, V.B. Voloshin, and V.I. Zakharov, Nucl. Phys. B229, 394 (1983).
63. L.S. Brown, R.D. Carlitz, and C. Lee, Phys. Rev. D 16, 417 (1977).
64. M. Atiyah and I. Singer, Ann. Math. 87, 484 (1968);
65. M. Atiyah, R. Bott, and V. Patodi, Invent. Math. 19, 279 (1973).
66. F. Ardalan and N. Sadooghi, Int. J. Mod. Phys. A 16, 3151 (2001).
67. J.M. Gracia-Bondia and C.P. Martin, Phys. Lett. B 479, 321 (2000).
68. C. Soo, Class. Quantum Grav. 18, 709 (2001).
69. L.S. Brown, R.D. Carlitz, D.B. Creamer, and C. Lee, Phys. Rev. D 17, 1583 (1978).
70. S. Cho, R. Hinterding, J. Madore, and H. Steinacker, Int. J. Mod. Phys. D 9, 161 (2000).
71. D.J. Gross and N.A. Nekrasov, J. High Energy Phys. 07, 034 (2000).
72. B.-H. Lee and H.S. Yang, "Propagators in noncommutative instantons," hep-th/0206001.