String theory and noncommutative geometry

Journal of High Energy Physics

Volumn 3, Issue 9, 1999, Pages

  Seiberg, Nathan ^a   Witten, Edward ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Bosonic strings; D branes; Gauge symmetry; Space time symmetries

Indexed keywords

EID: 0007084601     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/1999/09/032     Document Type: Article

References (105)

1. H.S. Snyder, Quantized space-time, Phys. Rev. 71 (1947) 38;
2. The electromagnetic field in quantized space-time, Phys. Rev. 72 (1947) 68.
3. A. Connes, Noncommutative geometry, Academic Press 1994.
4. A. Connes and M. Rieffel, Yang-Mills for noncommutative two-tori, in Operator algebras and mathematical physics Iowa City, Iowa, 1985, pp. 237 Contemp. Math. Oper. Alg. Math. Phys. 62, AMS 1987.
5. A. Connes, M.R. Douglas, and A. Schwarz, Noncommutative geometry and amatrix theory: compactification on tori, J. High Energy Phys. 02 (1998) 003 [hep-th/9711162].
6. T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M-theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043].
7. T. Banks, Nucl. Phys. 67 (Proc. Suppl.) (1998) 180 [hep-th/9710231];
8. D. Bigatti and L. Susskind, Review of matrix theory, hep-th/9712072.
9. B. de Wit, J. Hoppe and H. Nicolai, On the quantum mechanics of supermembranes, Nucl. Phys. B 305 (1988) 545.
10. J. Hoppe, Membranes and integrable systems, Phys. Lett. B 250 (1990) 44.
11. D.B. Fairlie, P. Fletcher and C.K. Zachos, Trigonometric structure constants for new infinite-dimensional algebras, Phys. Lett. B 218 (1989) 203;
12. Infinite dimensional algebras and a trigonometric basis for the classical Lie algebras, J. Math. Phys. 31 (1990) 1088.
13. A. H. Chamseddine and J. Froehlich, Some elements of Cannes' NC geometry, and space-time geometry, in Chen Ning Yang, a great physicist of the twentieth century, C.S. Liu and S.-T. Yau eds., Intl. Press, Boston 1995 [hep-th/9307012];
14. J. Froehlich and K. Gawedzki, Conformal field theory and geometry of strings, in Proc. of the conference on mathematical quantum theory Vancouver B.C. 1993, J. Feldman, R. Froese and L. Rosen eds., Centre de Recherche Mathematiques-Proc. and Lecture Notes, vol. 7 1994, p. 57, AMS Publ [hep-th/9310187];
15. A.H. Chamseddine and J. Froehlich, J. Math. Phys. 35 (1994) 5195 [hep-th/9406013];
16. J. Froehlich, O. Grandjean and A. Recknagel, Supersymmetric quantum theory, noncommutative geometry, and gravitation, Proc. of Les Houches Summer School 1995, A. Connes, K. Gawedzki and J. Zinn-Justin eds., Elsevier 1998 [hep-th/9706132].
17. E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253..
18. M. R. Douglas and C. Hull, D-Branes And The Noncommutative Torus, J. High Energy Phys. 02 (1998) 008 [hep-th/9711165].
19. Y.-K. E. Cheung and M. Krogh, Noncommutative geometry from 0-branes in a background B field, Nucl. Phys. B 528 (1998) 185 [hep-th/9803031].
20. C.-S. Chu and P.-M. Ho, Noncommutative open string and D-brane, Nucl. Phys. B 550 (1999) 151 [hep-th/9812219];
21. Constrained quantization of open string in background B field and noncommutative D-brane, hep-th/9906192.
22. V. Schomerus, D-branes and deformation quantization, J. High Energy Phys. 06 (1999) 030 [hep-th/9903205].
23. F. Ardalan, h. Arfaei and M.M. Sheikh-Jabbari, Mixed branes and M(atrix) theory on noncommutative torus, hep-th/9803067;
24. Noncommutative geometry from strings and branes, J. High Energy Phys. 02 (1999) 016 [hep-th/9810072];
25. Dirac quantization of open strings and noncommutativity in branes, hep-th/9906161 .
26. A. Schwarz, Marita equivalence and duality, Nucl. Phys. B 534 (1998) 720 [hep-th/9805034];
27. M.A. Rieffel and A. Schwarz, Marita equivalence of multidimensional noncommutative tori, math.QA/9803057;
28. M.A. Rieffel, J. Diff. Geom. 31 (1990) 535 [quant-ph/9712009].
29. A. Astashkevich, N. Nekrasov and A. Schwarz, On noncommutative Nahm transform, hep-th/9810147.
30. B. Morariu and B. Zuniino, Super-Yang-Mills on the noncommutative torus, hep-th/9807198;
31. D. Brace and B. Morariu, A note on the BPS spectrum of the matrix model, J. High Energy Phys. 02 (1999) 004 [hep-th/9810185];
32. D. Brace, B. Morariu, and B. Zuniino, Dualities of the matrix model from T duality of the type II string, Nucl. Phys. B 545 (1999) 192 [hep-th/9810099];
33. T duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B 549 (1999) 181 [hep-th/9811213].
34. C. Hofman and E. Verlinde, U duality of Born-Infeld on the noncommutative two torus, J. High Energy Phys. 12 (1998) 010 [hep-th/9810116];
35. Gauge bundles and Born-Infeld on the noncommutative torus, Nucl. Phys. B 547 (1999) 157 [hep-th/9810219].
36. B. Pioline and A. Schwarz, Marita equivalence and T-duality (or B versus ⊖), J. High Energy Phys. 08 (1999) 021 [hep-th/9908019].
37. A. Konechny and A. Schwarz, BPS states on noncommutative tori and duality, Nucl. Phys. B 550 (1999) 561 [hep-th/9811159];
38. Supersymmetry algebra and BPS states of super-Yang-Mills theories on noncommutative tori, Phys. Lett. B 453 (1999) 23 [hep-th/9901077];
39. 1/4 BPS states on noncommutative tori, J. High Energy Phys. 09 (1999) 030 [hep-th/9907008].
40. P. Ho and Y. Wu, Noncommutative geometry and D-branes, Phys. Lett. B 398 (1997) 52 [hep-th/9611233];
41. P.-M. Ho, Y.-Y. Wu and Y.-S. Wu, Towards a noncommutative geometric approach to matrix compactification, Phys. Rev. D 58 (1998) 026006 [hep-th/9712201];
42. P. Ho, Twisted bundle on quantum torus and BPS states in matrix theory, Phys. Lett. B 434 (1998) 41 [hep-th/9803166];
43. P. Ho and Y. Wu, Noncommutative gauge theories in Matrix theory, Phys. Rev. D 58 (1998) 066003 [hep-th/9801147].
44. M. Li, Comments on super-symmetric Yang-Mills theory on a noncommutative torus, hep-th/9802052.
45. T. Kawano and K. Okuyama, Matrix Theory on Noncommutative Torus, Phys. Lett. B 433 (1998) 29 [hep-th/9803044].
46. F. Lizzi and R.J. Szabo, Noncommutative geometry and space-time gauge symmetries of string theory, Chaos, Solitons, Fractals 10 (1999) 445 [hep-th/9712206];
47. G. Landi, F. Lizzi and R.J. Szabo, String geometry and the noncommutative torus, hep-th/9806099;
48. F. Lizzi and R.J. Szabo, Noncommutative geometry and string duality, hep-th/9904064.
49. R. Casalbuoni, Algebraic treatment of compactification on noncommutative tori, Phys. Lett. B 431 (1998) 69 [hep-th/9801170].
50. M. Kato and T. Kuroki, World volume noncommutativity versus target space noncommutativity, J. High Energy Phys. 03 (1999) 012 [hep-th/9902004].
51. D. Bigatti, Noncommutative geometry and super Yang-Mills Theory, Phys. Lett. B 451 (1999) 324 [hep-th/9804120].
52. D. Bigatti and L. Susskind, Magnetic fields, brunes and noncommutative geometry, hep-th/9908056.
53. A. Hashimoto and N. Itzhaki, Noncommutative Yang-Mills and the AdS / CFT correspondence, hep-th/9907166.
54. J.M. Maldacena and J.G. Russo, Large N limit of non-commutative gauge theories, J. High Energy Phys. 09 (1999) 025 [hep-th/9908134].
55. 4 from twisted (2,0) and little string theories, hep-th/9812172.
56. N. Seiberg, Phys. Lett. B 408 (1997) 98 [hep-th/9705221].
57. 4 and (2,0) superconformal field theory, Comm. Math. Phys. 198 (1998) 689 [hep-th/9802068].
58. M.R. Douglas and G. Moore, D-branes, quivers, and ALE instantons, hep-th/9603167.
59. O. Aharony, M. Berkooz, and N. Seiberg, Light cone description of (2,0) superconformal theories in six-dimensions, Adv. Theor. Math. Phys. 2 (1998) 119 [hep-th/9712117].
60. M. Berkooz, Nonlocal field theories and the noncommutative torus, Phys. Lett. B 430 (1998) 237 [hep-th/9802069].
61. E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541 [hep-th/9511030].
62. M. Douglas, Branes within branes, hep-th/9512077.
63. 4, in Topology, Geometry and Field Theory, World Scientific 1994.
64. E.S. Fradkin and A.A. Tseytlin, Nonlinear electrodynamics from quantized strings, Phys. Lett. B 163 (1985) 123.
65. C.G. Callan, C. Lovelace, C.R. Nappi, S.A. Yost, String loop corrections to beta functions, Nucl. Phys. B 288 (1987) 525;
66. A. Abouelsaood, C. G. Callan, C. R. Nappi and S.A. Yost, Open Strings In Background Gauge Fields, Nucl. Phys. B 280 (1987) 599.
67. ∞, and string field theory at c = 1, hep-th/9207011,
68. ∞ coherent states and path-integral derivation of bosonization of non-relativistic fermions in one dimension, hep-th/9309028,
69. ∞ algebra, hep-th/9403050.
70. D.B. Fairlie, T. Curtright, and C.K. Zachos, Integrable symplectic trilinear interactions for matrix membranes, Phys. Lett. B 405 (1997) 37 [hep-th/9704037];
71. D.B. Fairlie, Moyal brackets in M-Theory,Mod. Phys. Lett. A 13 (1998) 263 [hep-th/9707190];
72. Matrix membranes and integrability, hep-th/9709042.
73. C. Klimcik, Gauge theories on the noncommutative sphere, Comm. Math. Phys. 199 (1998) 257 [hep-th/9710153].
74. M. Kontsevich, Deformation quantization of Poisson manifolds, q-alg/9709040.
75. A.S. Cataneo and G. Felder, A path integral approach to the Kontsevich quantization formula, math.QA/9902090.
76. A.A. Tseytlin, Born-Infeld action, super-symmetry and string theory, to appear in the Yuri Golfand memorial volume, M. Shifman ed., World Scientific 2000, hep-th/9908105.
77. T. Banks and N. Seiberg, Nonperturbative infinities, Nucl. Phys. B 273 (1986) 157.
78. M. Henneaux, Lectures on the antifield-BRST formalism for gauge theories, Nucl. Phys. 18 (Proc. Suppl.) (1990) 47;
79. M. Henneaux and C. Teitelboim, Quantization of gauge systems Princeton University Press 1992.
80. J. Hughes and J. Polchinski, Partially broken global supersymmetry and the superstring, Nucl. Phys. B 278 (1986) 147.
81. J. Bagger and A. Galperin, A new goldstone multiplet for partially broken supersymmetry, Phys. Rev. D 55 (1997) 1091 [hep-th/9608177].
82. T. Filk, Divergencies in a field theory on quantum space, Phys. Lett. B 376 (1996) 53.
83. J.C. Varilly and J.M. Gracia-Bondia, On the ultraviolet behaviour of quantum fields over noncommutative manifolds, Int. J. Mod. Phys. A 14 (1999) 1305 [hep-th/9804001].
84. M. Chaichian, A. Demichev and P. Presnajder, Quantum field theory on noncommutative space-times and the persistence of ultraviolet divergences, hep-th/9812180;
85. q(2) symmetry, hep-th/9904132.
86. 4, Phys. Rev. Lett. 83 (1999) 476 [hep-th/9903077].
87. M.M. Sheikh-Jabbari, Renormalizability of the super symmetric Yang-Mills theories on the noncommutative torus, J. High Energy Phys. 06 (1999) 015 [hep-th/9903107].
88. T. Krajewski and R. Wulkenhaar, Perturbative quantum gauge fields on the noncommutative torus, hep-th/9903187.
89. S. Cho, R. Hinterding, J. Madore and H. Steinacker, Finite field theory on noncommutative geometries, hep-th/9903239.
90. E. Hawkins, Noncommutative regularization for the practical man, hep-th/9908052.
91. A. Sen, Tachyon condensation on the brane-antibrane system, J. High Energy Phys. 08 (1998) 012 [hep-th/9805170].
92. G. Moore, Finite in all directions, hep-th/9305139.
93. A. Connes, C*-algébres et géométrie différentielle, C. R. Acad. Se. Paris 290 (1980) 559.
94. M. Rieffei, 'Vector bundles' over higher dimensional 'noncommutative tori' , Proc. Conference Operator Algebras, Connections With Topology And Ergodic Theory, Lecture Notes In Math. 1132 456, Springer-Verlag 1985 .
95. R. Minasian and G. Moore, K theory and Ramond-Ramond charge, J. High Energy Phys. 11 (1997) 002 [hep-th/9710230].
96. E. Witten, D-branes and K theory, J. High Energy Phys. 12 (1998) 019 [hep-th/9810188].
97. S. Hellerman and J. Polchinski, unpublished.
98. N. Seiberg, Why is the matrix model correct? Phys. Rev. Lett. 79 (1997) 3577 [hep-th/9710009].
99. M. Douglas, D. Kabat, P. Pouliot, and S. Shenker, D-branes and short distances in string theory, Nucl. Phys. B 485 (1997) 85 [hep-th/9608024].
100. n and Matrix theory, Adv. Theor. Math. Phys. 2 (1998) 51 [hep-th/9709220].
101. M. Rozali, Phys. Lett. B 400 (1997) 260 [hep-th/9702136].
102. M. Berkooz, M. Rozali and N. Seiberg, Phys. Lett. B 408 (1997) 105 [hep-th/9704089].
103. M. Perry and J.H. Schwarz, Interacting chiral gauge fields in six-dimensions and BornInfeld theory, Nucl. Phys. B 489 (1997) 47 [hep-th/9611065].
104. P.S. Howe, E. Sezgin and P.C. West, Covariant field equations of the M-theory fivebrane, Phys. Lett. B 399 (1997) 49 [hep-th/9702008];
105. The six-dimensional self dual tensor, Phys. Lett. B 400 (1997) 255 [hep-th/9702111].