Anatomy of a duality

Nuclear Physics B

Volumn 521, Issue 1-2, 1998, Pages 71-116

  Johnson, Clifford V ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032527301     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00129-1     Document Type: Article

References (83)

1. [1] E. Witten, Five-branes and M-theory on an orbifold, Nucl. Phys. B 463 (1996) 383, hep-th/9512219.
2. [2] R. Güven, Black p-brane solutions of D = 11 supergravity theory, Phys. Lett. B 276 (1992) 49.
3. [3] E. Bergshoeff, E. Sezgin and P.K. Townsend, Supermembranes and eleven dimensional supergravity, Phys. Lett. B 189 (1987) 75; M.J. Duff and K.S. Stelle, Multimembrane solutions of D = 11 supergravity, Phys. Lett. B 253 (1991) 113.
4. [3] E. Bergshoeff, E. Sezgin and P.K. Townsend, Supermembranes and eleven dimensional supergravity, Phys. Lett. B 189 (1987) 75; M.J. Duff and K.S. Stelle, Multimembrane solutions of D = 11 supergravity, Phys. Lett. B 253 (1991) 113.
5. [4] M.J. Duff, Minasian and E. Witten, Evidence for heterotic/heterotic duality, Nucl. Phys. B 465 (1996) 413, hep-th/9601036.
6. [5] M.J. Duff, Strong/weak coupling duality from the dual string, Nucl. Phys. B 442 (1995) 47, hep-th/9501030; M.J. Duff, Putting string/string duality to the test, Nucl. Phys. B 436 (1995) 507, hep-th/9406198.
7. [5] M.J. Duff, Strong/weak coupling duality from the dual string, Nucl. Phys. B 442 (1995) 47, hep-th/9501030; M.J. Duff, Putting string/string duality to the test, Nucl. Phys. B 436 (1995) 507, hep-th/9406198.
8. [6] M. Berkooz, R.G. Leigh, J. Polchiaski, J. Schwarz, N. Seiberg and E. Witten, Anomalies, dualities, and topology of D = 6 N = 1 superstring vacua, Nucl. Phys. B 475 (1996) 115, hep-th/9605184.
9. [7] J. Dai, R.G. Leigh and J. Polchinski, New connections between string theories, Mod. Phys. Lett. A 4 (1989) 2073; P. Hořava, Background duality of open string models, Phys. Lett. B 231 (1989) 251; R.G. Leigh, Dirac-Born-Infeld action from Dirichlet sigma model, Mod. Phys. Lett. A 4 (1989) 2767; J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) 6041, hep-th/9407031.
10. [7] J. Dai, R.G. Leigh and J. Polchinski, New connections between string theories, Mod. Phys. Lett. A 4 (1989) 2073; P. Hořava, Background duality of open string models, Phys. Lett. B 231 (1989) 251; R.G. Leigh, Dirac-Born-Infeld action from Dirichlet sigma model, Mod. Phys. Lett. A 4 (1989) 2767; J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) 6041, hep-th/9407031.
11. [7] J. Dai, R.G. Leigh and J. Polchinski, New connections between string theories, Mod. Phys. Lett. A 4 (1989) 2073; P. Hořava, Background duality of open string models, Phys. Lett. B 231 (1989) 251; R.G. Leigh, Dirac-Born-Infeld action from Dirichlet sigma model, Mod. Phys. Lett. A 4 (1989) 2767; J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) 6041, hep-th/9407031.
12. [7] J. Dai, R.G. Leigh and J. Polchinski, New connections between string theories, Mod. Phys. Lett. A 4 (1989) 2073; P. Hořava, Background duality of open string models, Phys. Lett. B 231 (1989) 251; R.G. Leigh, Dirac-Born-Infeld action from Dirichlet sigma model, Mod. Phys. Lett. A 4 (1989) 2767; J. Polchinski, Combinatorics of boundaries in string theory, Phys. Rev. D 50 (1994) 6041, hep-th/9407031.
13. [8] A. Sagnotti, in Non-perturbative Quantum Field Theory, ed. G. Mack et al. (Pergamon, Oxford, 1988) p. 521; V. Periwal, unpublished; J. Govaerts, Phys. Lett. B 220 (1989) 77; P. Horǎva, Strings on world sheet orbifolds, Nucl. Phys. B 327 (1989) 461.
14. [8] A. Sagnotti, in Non-perturbative Quantum Field Theory, ed. G. Mack et al. (Pergamon, Oxford, 1988) p. 521; V. Periwal, unpublished; J. Govaerts, Phys. Lett. B 220 (1989) 77; P. Horǎva, Strings on world sheet orbifolds, Nucl. Phys. B 327 (1989) 461.
15. [8] A. Sagnotti, in Non-perturbative Quantum Field Theory, ed. G. Mack et al. (Pergamon, Oxford, 1988) p. 521; V. Periwal, unpublished; J. Govaerts, Phys. Lett. B 220 (1989) 77; P. Horǎva, Strings on world sheet orbifolds, Nucl. Phys. B 327 (1989) 461.
16. [8] A. Sagnotti, in Non-perturbative Quantum Field Theory, ed. G. Mack et al. (Pergamon, Oxford, 1988) p. 521; V. Periwal, unpublished; J. Govaerts, Phys. Lett. B 220 (1989) 77; P. Horǎva, Strings on world sheet orbifolds, Nucl. Phys. B 327 (1989) 461.
17. [9] E.G. Gimon and J. Polchinski, Consistency conditions of orientifolds and D-manifolds, Phys. Rev. D 54 (1996) 1667, hep-th/9601038.
18. [10] M. Bianchi and A. Sagnotti, Twist symmetry and open string Wilson lines, Nucl. Phys, B 361 (1991) 519.
19. [11] G. Aldazabal, A. Font, L.E. Ibanez and F. Quevedo, Heterotic/heterotic duality in D = 6, 4, Phys. Lett. B 380 (1996) 33, hep-th/9602097.
20. [12] T. Banks, W. Fischler, S. Shenker and L. Susskind, M-theory as a matrix model: A conjecture, Phys. Rev. D 55 (1997) 5112, hep-th/9610043.
21. [13] W. Taylor, D-brane field theory on compact spaces, Phys. Lett. B 394 (1997) 283, hep-th/9611042; O.J. Ganor, S. Ramgoolam and W. Taylor, Branes, fluxes and duality in M(atrix)-theory, Nucl. Phys. B 492 (1997) 191, hep-th/9611202.
22. [13] W. Taylor, D-brane field theory on compact spaces, Phys. Lett. B 394 (1997) 283, hep-th/9611042; O.J. Ganor, S. Ramgoolam and W. Taylor, Branes, fluxes and duality in M(atrix)-theory, Nucl. Phys. B 492 (1997) 191, hep-th/9611202.
23. [14] M. Rozali, Matrix theory and U-duality in seven dimensions, Phys. Lett. B 400 (1997) 260, hep-th/9702136.
24. 5, Phys. Lett. B 408 (1997) 105, hep-th/9704089.
25. [16] E.G. Gimon and C.V. Johnson, K3 orientifolds, Nucl. Phys. B 477 (1996) 715, hep-th/9604129.
26. [17] A. Dahbolkar and J. Park, Strings on orientifolds, Nucl. Phys. B 477 (1996) 701, hep-th/9604178.
27. [18] P. Horava and E. Witten, Heterotic and Type I string dynamics from eleven dimensions, Nucl. Phys. B 460 (1996) 506, hep-th/9510209.
28. [19] J. Polchinski, TASI Lectures on D-Branes, hep-th/9611050.
29. [20] J. Polchinski, S. Chaudhuri and C.V. Johnson, Notes on D-branes, hep-th/9602052.
30. [21] E. Bergshoeff, M. de Roo, M.B. Green, G. Papadopoulos and P.K. Townsend, Duality of Type II 7-branes and 8-branes, Nucl. Phys. B 470 (1996) 113, hep-th/9601150.
31. [22] L. Romans, Massive N = 2a supergravity in ten dimensions, Phys. Lett. B 169 (1986) 374.
32. [23] J. Polchinski, Dirichlet branes and Ramond-Ramond charges in string theory, Phys. Rev. Lett. 75 (1995) hep-th/9510017.
33. [24] E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85, hep-th/9503124.
34. [25] J. Polchinski and E. Witten, Evidence for Heterotic-Type I string duality, Nucl. Phys. B 460 (1996) 525, hep-th/9510169.
35. [26] C.M. Hull, String-string duality in ten dimensions, Phys. Lett. B 357 (1995) 545, hep-th/9506194.
36. [27] S.-J. Rey, Axionic string instantons and their low-energy implications, in Superstrings and Particle Theory, Proc., ed. L. Clavelli and B. Harms (World Scientific, Singapore, 1990); S.-J. Rey, The confining phase of superstrings and axionic strings, Phys. Rev. D 43 1991 526; A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167; B 353 (1991) 565 (E).
37. [27] S.-J. Rey, Axionic string instantons and their low-energy implications, in Superstrings and Particle Theory, Proc., ed. L. Clavelli and B. Harms (World Scientific, Singapore, 1990); S.-J. Rey, The confining phase of superstrings and axionic strings, Phys. Rev. D 43 1991 526; A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167; B 353 (1991) 565 (E).
38. [27] S.-J. Rey, Axionic string instantons and their low-energy implications, in Superstrings and Particle Theory, Proc., ed. L. Clavelli and B. Harms (World Scientific, Singapore, 1990); S.-J. Rey, The confining phase of superstrings and axionic strings, Phys. Rev. D 43 1991 526; A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167; B 353 (1991) 565 (E).
39. [27] S.-J. Rey, Axionic string instantons and their low-energy implications, in Superstrings and Particle Theory, Proc., ed. L. Clavelli and B. Harms (World Scientific, Singapore, 1990); S.-J. Rey, The confining phase of superstrings and axionic strings, Phys. Rev. D 43 1991 526; A. Strominger, Heterotic solitons, Nucl. Phys. B 343 (1990) 167; B 353 (1991) 565 (E).
40. [28] R. Dijkgraaf, E. Verlinde and H. Verlinde, Matrix string theory, Nucl. Phys. B 500 (1997) 43, hep-th/9703030.
41. [29] C.V. Johnson and R.C. Myers, Aspects of Type IIB theory on asymptotically locally euclidean spaces, Phys. Rev. D 55 (1997) 6382, hep-th/9610140.
42. 2, Phys. Lett. B 408 (1997) 98, hep-th/9705221.
43. [31] E. Witten, Sigma models and the ADHM construction of instantons, J. Geom. Phys. 15 (1995) 215, hep-th/9410052.
44. [32] M.R. Douglas, Gauge fields and D-branes, hep-th/9604198.
45. [33] M.R. Douglas, Branes within branes, hep-th/9512077.
46. [34] M.R. Douglas and G. Moore, D-branes, quivers and ALE instantons, hep-th/9603167.
47. [35] E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541, hep-th/9511030.
48. [36] J. Polchinski, Tensors from K3 orientifolds, hep-th/9606165.
49. [37] A. Sagnotti, A note on the Green-Schwarz mechanism in open-string theories, Phys. Lett. B 294 (1992) 196, hep-th/9210127.
50. [38] M. Dine, N. Seiberg and E. Witten, Fayet-Iliopoulos terms in string theory, Nucl. Phys. B 289 (1987) 589.
51. [39] N.J. Hitchin, A. Karlhede, U. Lindström and M. Roček, Hyper-Kähler metrics and supersymmetry, Comm. Math. Phys. 108 (1987) 535.
52. [40] M.F. Atiyah, V. Drinfeld, N.J. Hitchin and Y.I. Manin, Construction of instantons, Phys. Lett. A 65 (1978) 185.
53. [41] P.B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Diff. Geom. 29 (1989) 665.
54. [42] P.B. Kronheimer and H. Nakajima, Yang-Mills instantons on ALE gravitational instantons, Math. Ann. 288 (1990) 263.
55. [43] M. Bianchi, F. Fucito, G. Rossi and M. Martinelli, Explicit construction of Yang-Mills instantons on ALE spaces, Nucl. Phys. B 473 (1996) 367, hep-th/9601162.
56. [44] J. McKay, Graphs, singularities and finite groups, Proc. Symp. Pure. Math. 37 (1980) 183 (AMS, Providence, RI).
57. [45] N.J. Hitchin, Polygons and gravitons, Math. Proc. Camb. Phil. Soc. 85 (1979) 465.
58. [46] T. Eguchi and A.J. Hanson, Asymptotically flat self-dual solutions to euclidean gravity, Phys. Lett. B 74 (1978) 249.
59. [47] M.R. Douglas, H. Ooguri and S.H. Shenker, Issues in M(atrix) theory compactification, Phys. Lett. B 402 (1997) 36, hep-th/9702203; M.R. Douglas and H. Ooguri Why Matrix theory is hard, hep-th/9710178.
60. [47] M.R. Douglas, H. Ooguri and S.H. Shenker, Issues in M(atrix) theory compactification, Phys. Lett. B 402 (1997) 36, hep-th/9702203; M.R. Douglas and H. Ooguri Why Matrix theory is hard, hep-th/9710178.
61. [48] W. Fischler and A. Rajaraman, M(atrix) string theory on K3, hep-th/9704123.
62. 8 instantons in Matrix theory, hep-th/9709015; O. Aharony, M. Berkooz, S. Kachru and E. Silverstein, Matrix description of (1, 0) theories in six dimensions, hep-th/9709118.
63. 8 instantons in Matrix theory, hep-th/9709015; O. Aharony, M. Berkooz, S. Kachru and E. Silverstein, Matrix description of (1, 0) theories in six dimensions, hep-th/9709118.
64. [50] L. Motl, Proposals on non-perturbative superstring interactions, hep-th/9701025.
65. [51] T. Banks and N. Seiberg, Strings from matrices, hep-th/9702187.
66. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
67. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
68. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
69. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
70. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
71. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
72. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
73. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
74. [52] U.H. Danielsson and G. Ferretti, The heterotic life of the D-particle, Int. J. Mod. Phys. A 12 (1997) 4581, hep-th/9610082; S. Kachru and E. Silverstein, On gauge bosons in the Matrix model approach to M-theory, Phys. Lett. B 396 (1997) 70, hep-th/9612162; L. Motl, Quaternions and M(atrix) theory in spaces with boundaries, hep-th/9612198; N. Kim and S.-J. Rey, M(atrix) theory on an orbifold and twisted membrane, Nucl. Phys. B 504 (1997) 189; D. Lowe, Bound states of Type I' D-particles and enhanced gauge symmetry, Nucl. Phys. B 501 (1997) 134, hep-th/9702006; T. Banks, N. Seiberg and E. Silverstein, Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B 401 (1997) 30, hep-th/9703052; T. Banks and L. Motl, Heterotic strings from matrices, hep-th/9703218; D. Lowe, Heterotic matrix string theory, Phys. Lett. B 403 (1997) 243, hep-th/9704041; S.-J. Rey, Heterotic M(atrix) strings and their interactions, hep-th/9704158.
75. [53] P. Horava, Matrix theory and heterotic strings on tori, hep-th/9705055; D. Kabat and S.-J. Rey, Wilson lines and T-duality in heterotic M(atrix) theory, hep-th/9707099.
76. [53] P. Horava, Matrix theory and heterotic strings on tori, hep-th/9705055; D. Kabat and S.-J. Rey, Wilson lines and T-duality in heterotic M(atrix) theory, hep-th/9707099.
77. [54] S. Govindarajan, Heterotic M(atrix) theory at generic points in Narain moduli space, hep-th/9707164.
78. [55] M. Berkooz and M. Rozali, String dualities from Matrix theory, hep-th/9705175.
79. [56] D. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds - I, Nucl. Phys. B 473 (1996) 74, hep-th/9602114; D. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds - II, Nucl. Phys, B 476 (1996) 437, hep-th/9603161.
80. [56] D. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds - I, Nucl. Phys. B 473 (1996) 74, hep-th/9602114; D. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds - II, Nucl. Phys, B 476 (1996) 437, hep-th/9603161.
81. [57] E.G. Gimon and C.V. Johnson, Multiple realisations of script N = 1 vacua in six dimensions, Nucl. Phys. B 479 (1996) 285, hep-th/9606176.
82. [58] E. Gimon, private communication. See also Ref. [59].
83. [59] P. Berglund and E. Gimon, to appear.