The statistics of string/M theory vacua

Journal of High Energy Physics

Volumn 7, Issue 5, 2003, Pages 1077-1137

  Douglas, Michael R ^a,b  

^a RUTGERS UNIVERSITY   (United States)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

D branes; Random Systems; Superstring Vacua; Superstrings and Heterotic Strings

Indexed keywords

EID: 23044449480     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2003/05/046     Document Type: Review

References (89)

1. M.B. Green, J.H. Schwarz and E. Witten, Superstring theory, University Press, Cambridge 1987.
2. M.R. Douglas, How many vacua of superstring theory are there?, Lecture at JHS60, October 2001, Caltech. Available on the web at http://theory.caltech. edu.
3. M.R. Douglas, String compactification with N = 1 supersymmetry, in C. Bachas, A. Bilal, M. R. Douglas and N. A. Nekrasov, eds., Unity from duality: gravity, gauge theory and strings, Les Houches 2001, North Holland.
4. M.R. Douglas, B. Shiffman and S. Zelditch, work in progress.
5. M.R. Douglas, S. Ashok, and others, work in progress.
6. T. Banks, M. Dine and M.R. Douglas, Time-varying alpha and particle physics, Phys. Rev. Lett. 88 (2002) 131301 [hep-ph/0112059].
7. J. Polonyi, as referenced in [89].
8. T. Banks and L.J. Dixon, Constraints on string vacua with space-time super symmetry, Nucl. Phys. B 307 (1988) 93.
9. E. Witten, Constraints on supersymmetry breaking, Nucl. Phys. B 202 (1982) 253.
10. J. Wess and J. Bagger, Supersymmetry and Supergravity, Princeton University Press, Princeton 1990.
11. M.R. Douglas, Mastering N = 1, Lecture at Strings 2002, Cambridge UK. Available on the web at http://strings.cam.ac.uk
12. M.R. Douglas, Lectures on Dirichlet branes on Calabi-Yau manifolds, lectures at the 2001 Trieste spring school, available on the web at http://www.ictp.trieste.it.
13. J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136.
14. A.D. King, Moduli of representations of finite dimensional algebras, Quart. J. Math. Oxford 45 (2) (1994) 515.
15. M.R. Douglas, E. Witten and others, work in progress.
16. F. Cachazo, M.R. Douglas, N. Seiberg and E. Witten, Chiral rings and anomalies in supersymmetric gauge theory, J. High Energy Phys. 12 (2002) 071 [hep-th/0211170].
17. W. Fulton, Intersection theory, Springer-Verlag, Berlin 1998.
18. P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46.
19. M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117.
20. E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541 [hep-th/9511030].
21. B.R. Greene, String theory on Calabi-Yau manifolds, hep-th/9702155.
22. M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four dimensions, Adv. Theor. Math. Phys. 4 (2002) 1209 [hep-th/0002240].
23. R. Schimmrigk, Scaling behavior on the space of Calabi-Yau manifolds, alg-geom/9612012.
24. M. Gross, private communication.
25. P. Candelas, X.C. De La Ossa, P.S. Green and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991) 21.
26. G.W. Moore, Arithmetic and attractors, hep-th/9807087.
27. S. Kachru, M.B. Schulz and S. Trivedi, Moduli stabilization from fluxes in a simple iib orientifold, hep-th/0201028.
28. D.A. Cox and S. Katz, Mirror symmetry and algebraic geometry, American Mathematical Society (AMS), Providence 1999.
29. J.H. Horne and G.W. Moore, Chaotic coupling constants, Nucl. Phys. B 432 (1994) 109 [hep-th/9403058].
30. S.K. Donaldson and P.B. Kronheimer, The geometry of four-manifolds, Clarendon Press, Oxford 1990.
31. M.R. Douglas and C.-G. Zhou, to appear.
32. J. Polchinski, Lectures on D-branes, hep-th/9611050.
33. C.V. Johnson, D-brane primer, hep-th/0007170.
34. C. Angelantonj and A. Sagnotti, Open strings, Phys. Rept. 371 (2002) 1 [hep-th/0204089].
35. M. Cvetič, G. Shiu and A.M. Uranga, Chiral four-dimensional N = 1 supersymmetric type-IIA orientifolds from intersecting d6-branes, Nucl. Phys. B 615 (2001) 3 [hep-th/0107166].
36. M.R. Douglas and G.W. Moore, D-branes, quivers and ale instantons, hep-th/9603167.
37. D.-E. Diaconescu, M.R. Douglas and J. Gomis, Fractional branes and wrapped branes, J. High Energy Phys. 02 (1998) 013 [hep-th/9712230].
38. F. Cachazo, B. Fiol, K.A. Intriligator, S. Katz and C. Vafa, A geometric unification of dualities, Nucl. Phys. B 628 (2002) 3 [hep-th/0110028].
39. B. Fiol, Duality cascades and duality walls, J. High Energy Phys. 07 (2002) 058 [hep-th/0205155].
40. D. Gepner, Space-time supersymmetry in compactified string theory and superconformal models, Nucl. Phys. B 296 (1988) 757.
41. D.-E. Diaconescu and M.R. Douglas, D-branes on stringy Calabi-Yau manifolds, hep-th/0006224.
42. M.R. Douglas, S. Govindarajan, T. Jayaraman and A. Tomasiello, D-branes on Calabi-Yau manifolds and superpotentials, hep-th/0203173.
43. S. Katz, private communication.
44. C. Romelsberger, (Fractional) intersection numbers, tadpoles and anomalies, hep-th/0111086.
45. A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029].
46. F. Denef, Supergravity flows and D-brane stability, J. High Energy Phys. 08 (2000) 050 [hep-th/0005049].
47. C. Vafa, Black holes and Calabi-Yau threefolds, Adv. Theor. Math. Phys. 2 (1998) 207 [hep-th/9711067].
48. N. Seiberg, Electric-magnetic duality in supersymmetric nonabelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149].
49. C.E. Beasley and M.R. Plesser, Toric duality is seiberg duality, J. High Energy Phys. 12 (2001) 001 [hep-th/0109053].
50. B. Feng, A. Hanany, Y.-H. He and A.M. Uranga, Toric duality as seiberg duality and brane diamonds, J. High Energy Phys. 12 (2001) 035 [hep-th/0109063].
51. D. Berenstein and M.R. Douglas, Seiberg duality for quiver gauge theories, hep-th/0207027.
52. P.S. Aspinwall, B.R. Greene and D.R. Morrison, Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory, Nucl. Phys. B 416 (1994) 414 [hep-th/9309097].
53. B. Acharya, M. Aganagic, K. Hori and C. Vafa, Orientifolds, mirror symmetry and superpotentials, hep-th/0202208.
54. R.Y. Donagi, Principal bundles on elliptic fibrations, Asian J. Math. 1 (1997) 214-223 [alg-geom/9702002].
55. R. Friedman, J. W. Morgan, and E. Witten, Vector bundles over elliptic fibrations, J. Alg. Geom. 8 (1999) 279 [alg-geom/9709029].
56. A. Strominger, Superstrings with torsion, Nucl. Phys. B 274 (1986) 253.
57. J. Polchinski and A. Strominger, New vacua for type-II string theory, Phys. Lett. B 388 (1996) 736 [hep-th/9510227].
58. K. Becker and M. Becker, M-theory on eight-manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053].
59. K. Dasgupta, G. Rajesh and S. Sethi, M-theory, orientifolds and g-flux, J. High Energy Phys. 08 (1999) 023 [hep-th/9908088].
60. S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097].
61. B.S. Acharya, A moduli fixing mechanism in M-theory, hep-th/0212294.
62. S. Kachru, R. Kallosh, A. Linde and S.P. Trivedi, de Sitter vacua in string theory, hep-th/0301240.
63. R. Bousso and J. Polchinski, Quantization of four-form fluxes and dynamical neutralization of the cosmological constant, J. High Energy Phys. 06 (2000) 006 [hep-th/0004134].
64. J.L. Feng, J. March-Russell, S. Sethi and F. Wilczek, Saltatory relaxation of the cosmological constant, Nucl. Phys. B 602 (2001) 307 [hep-th/0005276].
65. S.R. Coleman and F. De Luccia, Gravitational effects on and of vacuum decay, Phys. Rev. D 21 (1980) 3305.
66. T. Banks, Heretics of the false vacuum: gravitational effects on and of vacuum decay, ii, hep-th/0211160.
67. J.D. Brown and C. Teitelboim, Neutralization of the cosmological constant by membrane creation, Nucl. Phys. B 297 (1988) 787.
68. P.K. Tripathy and S.P. Trivedi, Compactification with flux on K3 and tori, J. High Energy Phys. 03 (2003) 028 [hep-th/0301139].
69. S. Gukov, C. Vafa and E. Witten, CFT's from Calabi-Yau four-folds, Nucl. Phys. B 584 (2000) 69 [hep-th/9906070].
70. C. Vafa, Superstrings and topological strings at large-N, J. Math. Phys. 42 (2001) 2798 [hep-th/0008142].
71. S. Kobayashi, Hyperbolic complex spaces, Springer Verlag, Berlin 1998.
72. K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and α′-corrections to flux induced potentials, J. High Energy Phys. 06 (2002) 060 [hep-th/0204254].
73. P.S. Aspinwall and M.R. Douglas, D-brane stability and monodromy, J. High Energy Phys. 05 (2002) 031 [hep-th/0110071].
74. J.-C. Lee, T-dual RR zero-norm states, D-branes and S-duality of type-II string theory, hep-th/0007026.
75. B. Acharya, to appear.
76. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200].
77. R. Gopakumar and C. Vafa, On the gauge theory/geometry correspondence, Adv. Theor. Math. Phys. 3 (1999) 1415 [hep-th/9811131].
78. H. Ooguri and C. Vafa, Worldsheet derivation of a large-N duality, Nucl. Phys. B 641 (2002) 3 [hep-th/0205297].
79. F. Cachazo, N. Seiberg and E. Witten, Phases of N = 1 supersymmetric gauge theories and matrices, J. High Energy Phys. 02 (2003) 042 [hep-th/0301006].
80. F. Tanaka and S.F. Edwards, The ground state of a spin glass, J. Phys. F: Metal Phys. 10 (1980) 2769.
81. P. Bleher, B. Shiffman and S. Zelditch, Poincaré-Lelong approach to universality and scaling of correlations between zeroes, Commun. Math. Phys. 208 (2000) 771.
82. S. Zelditch, Asymptotics of polynomials and eigenfunctions, math. CA/0208104.
83. M.R. Douglas, B. Fiol and C. Romelsberger, The spectrum of BPS branes on a noncompact Calabi-Yau, hep-th/0003263.
84. L.E. Ibáñez, Standard model engineering with intersecting branes, hep-ph/0109082.
85. V.S. Kaplunovsky, One loop threshold effects in string unification, hep-th/9205070.
86. 2 holonomy, hep-th/0211269.
87. M. Cvetic, private communication.
88. Y. Shadmi and Y. Shirman, Dynamical supersymmetry breaking, Rev. Mod. Phys. 72 (2000) 25 [hep-th/9907225].
89. T. Banks, M. Dine and M. Graesser, Supersymmetry, axions and cosmology, hep-ph/0210256.