Noncommutative instantons in higher dimensions, vortices and topological K-cycles

Journal of High Energy Physics

Volumn 7, Issue 12, 2003, Pages 505-537

  Lechtenfeld, Olaf ^a   Popov, Alexander D ^a,b   Szabo, Richard J ^c  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^b JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^c HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

D branes; Integrable Field Theories; Non Commutative Geometry; Solitons Monopoles and Instantons

Indexed keywords

EID: 23044465746     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2003/12/022     Document Type: Article

References (83)

1. N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys. 09 (1999) 032 [hep-th/9908142].
2. J.A. Harvey, Komaba lectures on noncommutative solitons and D-branes, hep-th/0102076;
3. A. Konechny and A. Schwarz, Introduction to m(atrix) theory and noncommutative geometry, Phys. Rept. 360 (2002) 353 [hep-th/0012145] [hep-th/0107251];
4. M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048];
5. R. J. Szabo, Quantum field theory on noncommutative spaces, Phys. Rept. 378 (2003) 207 [hep-th/0109162].
6. A.A. Belavin, A.M. Polyakov, A.S. Shvarts and Y.S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett. B 59 (1975) 85.
7. E.B. Bogomolny, Stability of classical solutions, Sov. J. Nucl. Phys. 24 (1976) 449;
8. M.K. Prasad and C.M. Sommerfield, An exact classical solution for the 't Hooft monopole and the Julia-Zee dyon, Phys. Rev. Lett. 35 (1975) 760.
9. H.B. Nielsen and P. Olesen, Vortex-line models for dual strings, Nucl. Phys. B 61 (1973) 45.
10. C.H. Taubes, Arbitrary N-vortex solutions to the first order Landau-Ginzburg equations, Commun. Math. Phys. 72 (1980) 277;
11. On the equivalence of the first and second order equations for gauge theories, Commun. Math. Phys. 75 (1980) 207.
12. 4 and (2,0) superconformal six dimensional theory, Commun. Math. Phys. 198 (1998) 689 [hep-th/9802068].
13. D.J. Gross and N.A. Nekrasov, Solitons in noncommutative gauge theory, J. High Energy Phys. 03 (2001) 044 [hep-th/0010090].
14. D.P. Jatkar, G. Mandal and S.R. Wadia, Nielsen-Olesen vortices in noncommutative abelian Higgs model, J. High Energy Phys. 09 (2000) 018 [hep-th/0007078].
15. D. Bak, Exact multi-vortex solutions in noncommutative abelian-Higgs theory, Phys. Lett. B 495 (2000) 251 [hep-th/0008204];
16. D. Bak, K.-M. Lee and J.-H. Park, Noncommutative vortex solitons, Phys. Rev. D 63 (2001) 125010 [hep-th/0011099].
17. A.P. Polychronakos, Flux tube solutions in noncommutative gauge theories, Phys. Lett. B 495 (2000) 407 [hep-th/0007043].
18. D.J. Gross and N.A. Nekrasov, Dynamics of strings in noncommutative gauge theory, J. High Energy Phys. 10 (2000) 021 [hep-th/0007204].
19. M. Hamanaka, Noncommutative solitons and D-branes, hep-th/0303256;
20. F.A. Schaposnik, Noncommutative solitons and instantons, hep-th/0310202.
21. K. Dasgupta, S. Mukhi and G. Rajesh, Noncommutative tachyons, J. High Energy Phys. 06 (2000) 022 [hep-th/0005006];
22. J.A. Harvey, P. Kraus, F. Larsen and E.J. Martinec, D-branes and strings as non-commutative solitons, J. High Energy Phys. 07 (2000) 042 [hep-th/0005031].
23. Y. Matsuo, Topological charges of noncommutative soliton, Phys. Lett. B 499 (2001) 223 [hep-th/0009002].
24. J.A. Harvey and G.W. Moore, Noncommutative tachyons and K-theory, J. Math. Phys. 42 (2001) 2765 [hep-th/0009030].
25. R. Minasian and G.W. Moore, K-theory and Ramond-Ramond charge, J. High Energy Phys. 11 (1997) 002 [hep-th/9710230];
26. E. Witten, D-branes and K-theory, J. High Energy Phys. 12 (1998) 019 [hep-th/9810188];
27. P. Hořava, Type IIA D-branes, K-theory and matrix theory, Adv. Theor. Math. Phys. 2 (1999) 1373 [hep-th/9812135];
28. E. Witten, Overview of K-theory applied to strings, Int. J. Mod. Phys. A 16 (2001) 693 [hep-th/0007175].
29. K. Olsen and R.J. Szabo, Constructing D-branes from K-theory, Adv. Theor. Math. Phys. 3 (1999) 889 [hep-th/9907140].
30. E. Corrigan, C. Devchand, D.B. Fairlie and J. Nuyts, First order equations for gauge fields in spaces of dimension greater than four, Nucl. Phys. B 214 (1983) 452.
31. R.S. Ward, Completely solvable gauge field equations in dimension greater than four, Nucl. Phys. B 236 (1984) 381.
32. D.B. Fairlie and J. Nuyts, Spherically symmetric solutions of gauge theories in eight-dimensions, J. Phys. A 17 (1984) 2867;
33. S. Fubini and H. Nicolai, The octonionic instanton, Phys. Lett. B 155 (1985) 369;
34. A.D. Popov, Spherically symmetric solutions of Yang-Mills equations In D = 7 for arbitrary gauge group, Europhys. Lett. 17 (1992) 23;
35. Meron type solutions of the Yang-Mills equations in 4n-dimensions, Europhys. Lett. 19 (1992) 465;
36. T.A. Ivanova and A.D. Popov, Self-dual Yang-Mills fields in D = 7,8, octonions and Ward equations, Lett. Math. Phys. 24 (1992) 85;
37. (Anti)self-dual gauge fields in dimension D ≥ 4, Theor. Math. Phys. 84 (1993) 225;
38. M. Günaydin and H. Nicolai, Seven-dimensional octonionic Yang-Mills instanton and its extension to an heterotic string soliton, Phys. Lett. B 351 (1995) 169 [hep-th/9502009], addendum ibid. B376 (1996) 329;
39. E.G. Floratos and G.K. Leontaris, World volume supermembrane instantons in the light-cone frame, math.PH/0011027.
40. M. Mihailescu, I.Y. Park and T.A. Tran, D-branes as solitons of an N = 1, D = 10 non-commutative gauge theory, Phys. Rev. D 64 (2001) 046006 [hep-th/0011079];
41. E. Witten, BPS bound states of D0-D6 and D0-D8 systems in a B-field, J. High Energy Phys. 04 (2002) 012 [hep-th/0012054].
42. P. Kraus and M. Shigemori, Non-commutative instantons and the Seiberg-Witten map, J. High Energy Phys. 06 (2002) 034 [hep-th/0110035].
43. A. Fujii, Y. Imaizumi and N. Ohta, Supersymmetry, spectrum and fate of D0-Dp systems with B-field, Nucl. Phys. B 615 (2001) 61 [hep-th/0105079];
44. M. Hamanaka, Y. Imaizumi and N. Ohta, Moduli space and scattering of DO-branes in noncommutative super Yang-Mills theory, Phys. Lett. B 529 (2002) 163 [hep-th/0112050];
45. D.-S. Bak, K.-M. Lee and J.-H. Park, BPS equations in six and eight dimensions, Phys. Rev. D 66 (2002) 025021 [hep-th/0204221];
46. Y. Hiraoka, BPS solutions of noncommutative gauge theories in four and eight dimensions, hep-th/0205283;
47. Y. Hiraoka, Noncommutative U(1) instantons in eight dimensional Yang-Mills theory, Phys. Rev. D 67 (2003) 105025 [hep-th/0301176].
48. N.A. Nekrasov, Lectures on open strings and noncommutative gauge fields, hep-th/0203109.
49. S.K. Donaldson, Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. Lond. Math. Soc. 50 (1985) 1;
50. Infinite determinants, stable bundles and curvature, Duke Math. J. 54 (1987) 231.
51. K. Uhlenbeck and S.-T. Yau, On the existence of hermitian Yang-Mills connections in stable vector bundles, Commun. Pure Appl. Math. 39 (1986) 257.
52. O. Lechtenfeld and A.D. Popov, Noncommutative multi-solitons in 2 + 1 dimensions, J. High Energy Phys. 11 (2001) 040 [hep-th/0106213];
53. Scattering of noncommutative solitons in 2 + 1 dimensions, Phys. Lett. B 523 (2001) 178 [hep-th/0108118];
54. Noncommutative monopoles and Riemann-Hilbert problems, hep-th/0306263;
55. Z. Horvath, O. Lechtenfeld and M. Wolf, Noncommutative instantons via dressing and splitting approaches, J. High Energy Phys. 12 (2002) 060 [hep-th/0211041].
56. E. Witten, Some exact multi-pseudoparticle solutions of classical Yang-Mills theory, Phys. Rev. Lett. 38 (1977) 121.
57. D.H. Correa, E.F. Moreno and F.A. Schaposnik, Some noncommutative multi-instantons from vortices in curved space, Phys. Lett. B 543 (2002) 235 [hep-th/0207180].
58. P. Forgacs and N.S. Manton, Space-time symmetries in gauge theories, Commun. Math. Phys. 72 (1980) 15.
59. T.T. Wu and C.N. Yang, Concept of nonintegrable phase factors and global formulation of gauge fields, Phys. Rev. D 12 (1975) 3845.
60. F.A. Bais, SO(3) monopoles and dyons with multiple magnetic charge, Phys. Lett. B 64 (1976) 465.
61. E. Corrigan, D.I. Olive, D.B. Fairlie and J. Nuyts, Magnetic monopoles in SU(3) gauge theories, Nucl. Phys. B 106 (1976) 475.
62. O. Garcia-Prada, Invariant connections and vortices, Commun. Math. Phys. 156 (1993) 527;
63. Dimensional reduction of stable bundles, vortices and stable pairs, Int. J. Math. 5 (1994) 1.
64. S.B. Bradlow and O. Garcia-Prada, Non-abelian monopoles and vortices, alg-geom/9602010.
65. 4, J. Math. Phys. 44 (2003) 4527 [hep-th/0304263].
66. M. Aganagic, R. Gopakumar, S. Minwalla and A. Strominger, Unstable solitons in noncommutative gauge theory, J. High Energy Phys. 04 (2001) 001 [hep-th/0009142];
67. J.A. Harvey, P. Kraus and F. Larsen, Exact noncommutative solitons, J. High Energy Phys. 12 (2000) 024 [hep-th/0010060].
68. O. Lechtenfeld and A.D. Popov, Noncommutative 't Hooft instantons, J. High Energy Phys. 03 (2002) 040 [hep-th/0109209].
69. 2, Phys. Lett. B 567 (2003) 107 [hep-th/0305195].
70. A. Jaffe and C. Taubes, Vortices and monopoles, Birkhaüser, Boston 1980.
71. K. Dasgupta and S. Mukhi, Brane constructions, fractional branes and anti-de Sitter domain walls, J. High Energy Phys. 07 (1999) 008 [hep-th/9904131].
72. R. Tatar, A note on non-commutative field theory and stability of brane-antibrane systems, hep-th/0009213;
73. L. Dolan and C.R. Nappi, A scaling limit with many noncommutativity parameters, Phys. Lett. B 504 (2001) 329 [hep-th/0009225];
74. K. Dasgupta and Z. Yin, Non-abelian geometry, Commun. Math. Phys. 235 (2003) 313 [hep-th/0011034];
75. K. Dasgupta and M. Shmakova, On branes and oriented B-fields, Nucl. Phys. B 675 (2003) 205 [hep-th/0306030].
76. P. Baum and R.G. Douglas, K-homology and index theory, Proc. Symp. Pure Math. 38 (1982) 117.
77. T. Asakawa, S. Sugimoto and S. Terashima, D-branes, matrix theory and K-homology, J. High Energy Phys. 03 (2002) 034 [hep-th/0108085];
78. R.J. Szabo, D-branes, tachyons and K-homology, Mod. Phys. Lett. A 17 (2002) 2297 [hep-th/0209210].
79. M. Jakob, A bordism-type description of homology, Manuscripta Math. 96 (1998) 67.
80. M. Karoubi, K-theory, Springer, Berlin 1978.
81. D.-E. Diaconescu, G.W. Moore and E. Witten, E(8) gauge theory and a derivation of K-theory from M-theory, Adv. Theor. Math. Phys. 6 (2003) 1031 [hep-th/0005090].
82. M. Alishahiha, H. Ita and Y. Oz, On superconnections and the tachyon effective action, Phys. Lett. B 503 (2001) 181 [hep-th/0012222];
83. R.J. Szabo, Superconnections, anomalies and non-BPS brane charges, J. Geom. Phys. 43 (2002) 241 [hep-th/0108043].