Generalized N = 1 orientifold compactifications and the Hitchin functionals

Nuclear Physics B

Volumn 748, Issue 1-2, 2006, Pages 200-252

  Benmachiche, Iman ^a,b   Grimm, Thomas W ^c  

^a DESY   (Germany)

^b UNIVERSITY OF HAMBURG   (Germany)

^c University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745268872     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2006.05.003     Document Type: Article

References (174)

1. For a review see, for example. Kiritsis E. D-branes in standard model building, gravity and cosmology. Fortschr. Phys. 52 (2004) 200. hep-th/0310001
2. Uranga A.M. Chiral four-dimensional string compactifications with intersecting D-branes. Class. Quantum Grav. 20 (2003) S373. hep-th/0301032
3. Lüst D. Intersecting brane worlds: A path to the standard model?. Class. Quantum Grav. 21 (2004) S1399. hep-th/0401156
4. Ibáñez L.E. The fluxed MSSM. Phys. Rev. D 71 (2005) 055005. hep-ph/0408064
5. Blumenhagen R. Recent progress in intersecting D-brane models. hep-th/0412025
6. Blumenhagen R., Cvetic M., Langacker P., and Shiu G. Toward realistic intersecting D-brane models. hep-th/0502005 and references therein
7. For a review see, for example. Linde A. Prospects of inflation. hep-th/0402051
8. Balasubramanian V. Accelerating universes and string theory. Class. Quantum Grav. 21 (2004) S1337. hep-th/0404075
9. Burgess C.P. Inflationary string theory?. hep-th/0408037
10. Linde A.D. Particle physics and inflationary cosmology. hep-th/0503203 and references therein
11. Sagnotti A. Open strings and their symmetry groups. hep-th/0208020
12. Dai J., Leigh R.G., and Polchinski J. New connections between string theories. Mod. Phys. Lett. A 4 (1989) 2073
13. Leigh R.G. Dirac-Born-Infeld action from Dirichlet sigma model. Mod. Phys. Lett. A 4 (1989) 2767
14. Bianchi M., and Sagnotti A. On the systematics of open string theories. Phys. Lett. B 247 (1990) 517
15. Bianchi M., and Sagnotti A. Twist symmetry and open string Wilson lines. Nucl. Phys. B 361 (1991) 519
16. Horava P. Strings on world sheet orbifolds. Nucl. Phys. B 327 (1989) 461
17. Polchinski J. Dirichlet-branes and Ramond-Ramond charges. Phys. Rev. Lett. 75 (1995) 4724. hep-th/9510017
18. Gimon E.G., and Polchinski J. Consistency conditions for orientifolds and D-manifolds. Phys. Rev. D 54 (1996) 1667. hep-th/9601038
19. Polchinski J. String Theory vols. 1 and 2 (1998), Cambridge Univ. Press, Cambridge
20. For a review see, for example. Dabholkar A. Lectures on orientifolds and duality. hep-th/9804208
21. Angelantonj C., and Sagnotti A. Open strings. Phys. Rep. 371 (2002) 1. hep-th/0204089
22. Angelantonj C., and Sagnotti A. Phys. Rep. 376 (2003) 339 Erratum
23. Angelantonj C., Bianchi M., Pradisi G., Sagnotti A., and Stanev Y.S. Chiral asymmetry in four-dimensional open-string vacua. Phys. Lett. B 385 (1996) 96. hep-th/9606169
24. Berkooz M., and Leigh R.G. A D = 4, N = 1 orbifold of type I strings. Nucl. Phys. B 483 (1997) 187. hep-th/9605049
25. Aldazabal G., Font A., Ibáñez L.E., and Violero G. D = 4, N = 1, type IIB orientifolds. Nucl. Phys. B 536 (1998) 29. hep-th/9804026
26. Cvetic M., Shiu G., and Uranga A.M. Chiral four-dimensional N = 1 supersymmetric type IIA orientifolds from intersecting D6-branes. Nucl. Phys. B 615 (2001) 3. hep-th/0107166
27. Giddings S.B., Kachru S., and Polchinski J. Hierarchies from fluxes in string compactifications. Phys. Rev. D 66 (2002) 106006. hep-th/0105097
28. Acharya B., Aganagic M., Hori K., and Vafa C. Orientifolds, mirror symmetry and superpotentials. hep-th/0202208
29. Blumenhagen R., Braun V., Körs B., and Lüst D. Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes. JHEP 0207 (2002) 026. hep-th/0206038
30. Blumenhagen R., Braun V., Körs B., and Lüst D. The standard model on the quintic. hep-th/0210083
31. Brunner I., and Hori K. Orientifolds and mirror symmetry. JHEP 0411 (2004) 005. hep-th/0303135
32. Brunner I., Hori K., Hosomichi K., and Walcher J. Orientifolds of Gepner models. hep-th/0401137
33. For a review see, for example. Graña M. Flux compactifications in string theory: A comprehensive review. Phys. Rep. 423 (2006) 91. hep-th/0509003 and references therein
34. Curio G., Klemm A., Lust D., and Theisen S. On the vacuum structure of type II string compactifications on Calabi-Yau spaces with H-fluxes. Nucl. Phys. B 609 (2001) 3. hep-th/0012213
35. Kachru S., Schulz M.B., and Trivedi S. Moduli stabilization from fluxes in a simple IIB orientifold. JHEP 0310 (2003) 007. hep-th/0201028
36. Blumenhagen R., Lüst D., and Taylor T.R. Moduli stabilization in chiral type IIB orientifold models with fluxes. Nucl. Phys. B 663 (2003) 319. hep-th/0303016
37. Curio G., Krause A., and Lust D. Moduli stabilization in the heterotic/IIB discretuum. hep-th/0502168
38. Denef F., Douglas M.R., Florea B., Grassi A., and Kachru S. Fixing all moduli in a simple F-theory compactification. hep-th/0503124
39. Lust D., Reffert S., Schulgin W., and Stieberger S. Moduli stabilization in type IIB orientifolds. I: Orbifold limits. hep-th/0506090
40. Derendinger J.P., Kounnas C., Petropoulos P.M., and Zwirner F. Superpotentials in IIA compactifications with general fluxes. Nucl. Phys. B 715 (2005) 211. hep-th/0411276
41. Derendinger J.P., Kounnas C., Petropoulos P.M., and Zwirner F. Fluxes and gaugings: N = 1 effective superpotentials. Fortschr. Phys. 53 (2005) 926. hep-th/0503229
42. Villadoro G., and Zwirner F. N = 1 effective potential from dual type-IIA D6/O6 orientifolds with general fluxes. JHEP 0506 (2005) 047. hep-th/0503169
43. DeWolfe O., Giryavets A., Kachru S., and Taylor W. Type IIA moduli stabilization. JHEP 0507 (2005) 066. hep-th/0505160
44. Camara P.G., Font A., and Ibanez L.E. Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold. JHEP 0509 (2005) 013. hep-th/0506066
45. ′-corrections to flux induced potentials. JHEP 0206 (2002) 060. hep-th/0204254
46. Grimm T.W., and Louis J. The effective action of N = 1 Calabi-Yau orientifolds. Nucl. Phys. B 699 (2004) 387. hep-th/0403067
47. Grimm T.W., and Louis J. The effective action of type IIA Calabi-Yau orientifolds. Nucl. Phys. B 718 (2005) 153. hep-th/0412277
48. Graña M. MSSM parameters from supergravity backgrounds. Phys. Rev. D 67 (2003) 066006. hep-th/0209200
49. Körs B., and Nath P. Effective action and soft supersymmetry breaking for intersecting D-brane models. Nucl. Phys. B 681 (2004) 77. hep-th/0309167
50. Cámara P.G., Ibáñez L.E., and Uranga A.M. Flux-induced SUSY-breaking soft terms. Nucl. Phys. B 689 (2004) 195. hep-th/0311241
51. Graña M., Grimm T.W., Jockers H., and Louis J. Soft supersymmetry breaking in Calabi-Yau orientifolds with D-branes and fluxes. Nucl. Phys. B 690 (2004) 21. hep-th/0312232
52. Lawrence A., and McGreevy J. Local string models of soft supersymmetry breaking. hep-th/0401034
53. Lawrence A., and McGreevy J. Remarks on branes, fluxes, and soft SUSY breaking. hep-th/0401233
54. Lüst D., Mayr P., Richter R., and Stieberger S. Scattering of gauge, matter, and moduli fields from intersecting branes. Nucl. Phys. B 696 (2004) 205. hep-th/0404134
55. Lust D., Reffert S., and Stieberger S. Flux-induced soft supersymmetry breaking in chiral type IIb orientifolds with D3/D7-branes. Nucl. Phys. B 706 (2005) 3. hep-th/0406092
56. Cámara P.G., Ibáñez L.E., and Uranga A.M. Flux-induced SUSY-breaking soft terms on D7-D3 brane systems. Nucl. Phys. B 708 (2005) 268. hep-th/0408036
57. Lust D., Reffert S., and Stieberger S. MSSM with soft SUSY breaking terms from D7-branes with fluxes. Nucl. Phys. B 727 (2005) 264. hep-th/0410074
58. Font A., and Ibanez L.E. SUSY-breaking soft terms in a MSSM magnetized D7-brane model. JHEP 0503 (2005) 040. hep-th/0412150
59. Lust D., Mayr P., Reffert S., and Stieberger S. F-theory flux, destabilization of orientifolds and soft terms on D7-branes. Nucl. Phys. B 732 (2006) 243. hep-th/0501139
60. Choi K., Falkowski A., Nilles H.P., and Olechowski M. Soft supersymmetry breaking in KKLT flux compactification. Nucl. Phys. B 718 (2005) 113. hep-th/0503216
61. Bertolini M., Billo M., Lerda A., Morales J.F., and Russo R. Brane world effective actions for D-branes with fluxes. hep-th/0512067
62. Chen C.M., Li T., and Nanopoulos D.V. Type IIA Pati-Salam flux vacua. hep-th/0601064
63. Frey A.R. Warped strings: Self-dual flux and contemporary compactifications. hep-th/0308156
64. Jockers H. The effective action of D-branes in Calabi-Yau orientifold compactifications. Fortschr. Phys. 53 (2005) 1087. hep-th/0507042
65. Grimm T.W. The effective action of type II Calabi-Yau orientifolds. Fortschr. Phys. 53 (2005) 1179. hep-th/0507153
66. 2 structures. Differential Geometry, Valencia, 2001 (2002), World Sci. Publishing 115. math.DG/0202282
67. Salamon S. Riemannian Geometry and Holonomy Groups. Pitman Research Notes in Mathematics vol. 201 (1989), Longman, Harlow
68. Joyce D. Compact Manifolds with Special Holonomy (2000), Oxford Univ. Press, Oxford
69. Rocek M. Modified Calabi-Yau manifolds with torsion. In: Yau S.T. (Ed). Essays on Mirror Manifolds (1992), International Press, Hong Kong
70. Gates S.J., Hull C.M., and Rocek M. Twisted multiplets and new supersymmetric nonlinear sigma models. Nucl. Phys. B 248 (1984) 157
71. Strominger A. Superstrings with torsion. Nucl. Phys. B 274 (1986) 253
72. C.M. Hull, Superstring compactifications with torsion and space-time supersymmetry, in: Turin 1985, Proceedings, Superunification and Extra Dimensions, pp. 347-375
73. Hull C.M. Compactifications of the heterotic superstring. Phys. Lett. B 178 (1986) 357
74. Gauntlett J.P., Kim N.W., Martelli D., and Waldram D. Fivebranes wrapped on SLAG three-cycles and related geometry. JHEP 0111 (2001) 018. hep-th/0110034
75. Gauntlett J.P., Martelli D., Pakis S., and Waldram D. G-structures and wrapped NS5-branes. hep-th/0205050
76. Gauntlett J.P., Martelli D., and Waldram D. Superstrings with intrinsic torsion. Phys. Rev. D 69 (2004) 086002. hep-th/0302158
77. Gurrieri S., Louis J., Micu A., and Waldram D. Mirror symmetry in generalized Calabi-Yau compactifications. Nucl. Phys. B 654 (2003) 61. hep-th/0211102
78. Gurrieri S., and Micu A. Type IIB theory on half-flat manifolds. Class. Quantum Grav. 20 (2003) 2181. hep-th/0212278
79. Cardoso G.L., Curio G., Dall'Agata G., Lust D., Manousselis P., and Zoupanos G. Non-Kaehler string backgrounds and their five torsion classes. Nucl. Phys. B 652 (2003) 5. hep-th/0211118
80. Kachru S., Schulz M.B., Tripathy P.K., and Trivedi S.P. New supersymmetric string compactifications. JHEP 0303 (2003) 061. hep-th/0211182
81. Kaste P., Minasian R., Petrini M., and Tomasiello A. Kaluza-Klein bundles and manifolds of exceptional holonomy. JHEP 0209 (2002) 033. hep-th/0206213
82. Kaste P., Minasian R., Petrini M., and Tomasiello A. Nontrivial RR two-form field strength and SU (3)-structure. Fortschr. Phys. 51 (2003) 764. hep-th/0301063
83. Cardoso G.L., Curio G., Dall'Agata G., and Lüst D. BPS action and superpotential for heterotic string compactifications with fluxes. JHEP 0310 (2003) 004. hep-th/0306088
84. Becker K., Becker M., Dasgupta K., and Green P.S. Compactifications of heterotic theory on non-Kähler complex manifolds. I. JHEP 0304 (2003) 007. hep-th/0301161
85. Becker K., Becker M., Green P.S., Dasgupta K., and Sharpe E. Compactifications of heterotic strings on non-Kähler complex manifolds. II. Nucl. Phys. B 678 (2004) 19. hep-th/0310058
86. Becker M., Dasgupta K., Knauf A., and Tatar R. Geometric transitions, flops and non-Kähler manifolds. I. Nucl. Phys. B 702 (2004) 207. hep-th/0403288
87. Alexander S., Becker K., Becker M., Dasgupta K., Knauf A., and Tatar R. In the realm of the geometric transitions. Nucl. Phys. B 704 (2005) 231. hep-th/0408192
88. Becker M., Dasgupta K., Katz S., Knauf A., and Tatar R. Geometric transitions, flops and non-Kaehler manifolds. II. Nucl. Phys. B 738 (2006) 124. hep-th/0511099
89. Behrndt K., and Jeschek C. Fluxes in M-theory on 7-manifolds and G structures. JHEP 0304 (2003) 002. hep-th/0302047
90. Behrndt K., and Jeschek C. Fluxes in M-theory on 7-manifolds: G-structures and superpotential. Nucl. Phys. B 694 (2004) 99. hep-th/0311119
91. Fidanza S., Minasian R., and Tomasiello A. Mirror symmetric SU (3)-structure manifolds with NS fluxes. Commun. Math. Phys. 254 (2005) 401. hep-th/0311122
92. Dall'Agata G. On supersymmetric solutions of type IIB supergravity with general fluxes. Nucl. Phys. B 695 (2004) 243. hep-th/0403220
93. Frey A.R. Notes on SU (3) structures in type IIB supergravity. JHEP 0406 (2004) 027. hep-th/0404107
94. Jeschek C. Generalized Calabi-Yau structures and mirror symmetry. hep-th/0406046
95. Chiantese S., Gmeiner F., and Jeschek C. Mirror symmetry for topological sigma models with generalized Kaehler geometry. hep-th/0408169
96. Graña M., Minasian R., Petrini M., and Tomasiello A. Supersymmetric backgrounds from generalized Calabi-Yau manifolds. JHEP 0408 (2004) 046. hep-th/0406137
97. 2-structures and type IIB superstrings. JHEP 0503 (2005) 053. hep-th/0412280
98. Kapustin A., and Li Y. Topological sigma-models with H-flux and twisted generalized complex manifolds. hep-th/0407249
99. Behrndt K., and Cvetic M. General N = 1 supersymmetric fluxes in massive type IIA string theory. Nucl. Phys. B 708 (2005) 45. hep-th/0407263
100. Lüst D., and Tsimpis D. Supersymmetric AdS(4) compactifications of IIA supergravity. JHEP 0502 (2005) 027. hep-th/0412250
101. Gurrieri S., Lukas A., and Micu A. Heterotic on half-flat. Phys. Rev. D 70 (2004) 126009. hep-th/0408121
102. Zucchini R. A sigma model field theoretic realization of Hitchin's generalized complex geometry. JHEP 0411 (2004) 045. hep-th/0409181
103. Zucchini R. Generalized complex geometry, generalized branes and the Hitchin sigma model. JHEP 0503 (2005) 022. hep-th/0501062
104. 2 structure. Class. Quantum Grav. 22 (2005) 1709. hep-th/0412006
105. Dall'Agata G., and Ferrara S. Gauged supergravity algebras from twisted tori compactifications with fluxes. Nucl. Phys. B 717 (2005) 223. hep-th/0502066
106. Tomasiello A. Topological mirror symmetry with fluxes. hep-th/0502148
107. Behrndt K., Cvetic M., and Gao P. General type IIB fluxes with SU (3) structures. hep-th/0502154
108. Pestun V., and Witten E. The Hitchin functionals and the topological B-model at one loop. Lett. Math. Phys. 74 (2005) 21. hep-th/0503083
109. Pestun V. Black hole entropy and topological strings on generalized CY manifolds. hep-th/0512189
110. Dall'Agata G., D'Auria R., and Ferrara S. Compactifications on twisted tori with fluxes and free differential algebras. hep-th/0503122
111. Hull C.M., and Reid-Edwards R.A. Flux compactifications of string theory on twisted tori. J. Sci. Eng. 1 (2004) 411. hep-th/0503114
112. 7 (7) symmetry and dual gauge algebra of M-theory on a twisted seven-torus. hep-th/0504108
113. Andrianopoli L., Lledo M.A., and Trigiante M. The Scherk-Schwarz mechanism as a flux compactification with internal torsion. JHEP 0505 (2005) 051. hep-th/0502083
114. Berglund P., and Mayr P. Non-perturbative superpotentials in F-theory and string duality. hep-th/0504058
115. House T., and Palti E. Effective action of (massive) IIA on manifolds with SU (3) structure. hep-th/0505177
116. Grana M., Minasian R., Petrini M., and Tomasiello A. Generalized structures of N = 1 vacua. JHEP 0511 (2005) 020. hep-th/0505212
117. Grana M., Louis J., and Waldram D. Hitchin functionals in N = 2 supergravity. JHEP 0601 (2006) 008. hep-th/0505264
118. Koerber P. Stable D-branes, calibrations and generalized Calabi-Yau geometry. JHEP 0508 (2005) 099. hep-th/0506154
119. Martucci L., and Smyth P. Supersymmetric D-branes and calibrations on general N = 1 backgrounds. JHEP 0511 (2005) 048. hep-th/0507099
120. Martucci L. D-branes on general N = 1 backgrounds: Superpotentials and D-terms. hep-th/0602129
121. Dall'Agata G., and Prezas N. Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes. JHEP 0510 (2005) 103. hep-th/0509052
122. Chuang W.y., Kachru S., and Tomasiello A. Complex/symplectic mirrors. hep-th/0510042
123. Jeschek C., and Witt F. Generalised geometries, constrained critical points and Ramond-Ramond fields. math.DG/0510131
124. Tsimpis D. M-theory on eight-manifolds revisited: N = 1 supersymmetry and generalized Spin(7) structures. hep-th/0511047
125. Behrndt K., Cvetic M., and Liu T. Classification of supersymmetric flux vacua in M theory. hep-th/0512032
126. Dall'Agata G. Non-Kaehler attracting manifolds. hep-th/0602045
127. Hsu J.P., Maloney A., and Tomasiello A. Black hole attractors and pure spinors. hep-th/0602142
128. Anguelova L., and Zoubos K. Flux superpotential in heterotic M-theory. hep-th/0602039
129. Micu A., Palti E., and Saffin P.M. M-theory on seven-dimensional manifolds with SU (3) structure. hep-th/0602163
130. Shelton J., Taylor W., and Wecht B. Nongeometric flux compactifications. JHEP 0510 (2005) 085. hep-th/0508133
131. Aldazabal G., Camara P.G., Font A., and Ibanez L.E. More dual fluxes and moduli fixing. hep-th/0602089
132. Villadoro G., and Zwirner F. D terms from D-branes, gauge invariance and moduli stabilization in flux compactifications. hep-th/0602120
133. Andrianopoli L., D'Auria R., and Ferrara S. Supersymmetry reduction of N-extended supergravities in four dimensions. JHEP 0203 (2002) 025. hep-th/0110277
134. Andrianopoli L., D'Auria R., and Ferrara S. Consistent reduction of N = 2 → N = 1 four-dimensional supergravity coupled to matter. Nucl. Phys. B 628 (2002) 387. hep-th/0112192
135. D'Auria R., Ferrara S., Trigiante M., and Vaula S. N = 1 reductions of N = 2 supergravity in the presence of tensor multiplets. JHEP 0503 (2005) 052. hep-th/0502219
136. Hitchin N.J. The geometry of three-forms in six and seven dimensions. math.DG/0010054
137. Hitchin N.J. The geometry of three forms in six dimensions. J. Diff. Geom. 55 (2000) 547
138. Hitchin N.J. Stable forms and special metrics. math.DG/0107101
139. Hitchin N. Generalized Calabi-Yau manifolds. Quart. J. Math. Oxford Ser. 54 (2003) 281. math.DG/0209099
140. Hitchin N. Brackets, forms and invariant functionals. math.DG/0508618
141. Mathai V., and Rosenberg J.M. T-duality for torus bundles via noncommutative topology. Commun. Math. Phys. 253 (2004) 705. hep-th/0401168
142. Mathai V., and Rosenberg J.M. On mysteriously missing T-duals, H-flux and the T-duality group. hep-th/0409073
143. Bouwknegt P., Hannabuss K., and Mathai V. T-duality for principal torus bundles and dimensionally reduced Gysin sequences. hep-th/0412268
144. Mathai V., and Rosenberg J. T-duality for torus bundles with H-fluxes via noncommutative topology. II: The high-dimensional case and the T-duality group. hep-th/0508084
145. Hull C.M. A geometry for non-geometric string backgrounds. JHEP 0510 (2005) 065. hep-th/0406102
146. Dabholkar A., and Hull C. Generalised T-duality and non-geometric backgrounds. hep-th/0512005
147. Gualtieri M. Generalized complex geometry, Oxford University DPhil thesis. math.DG/0401221 pp. 107
148. Witt F. Special metric structures and closed forms. math.DG/0502443
149. Work in preparation
150. Strominger A., Yau S.T., and Zaslow E. Mirror symmetry is T-duality. Nucl. Phys. B 479 (1996) 243. hep-th/9606040
151. Giddings S.B., and Maharana A. Dynamics of warped compactifications and the shape of the warped landscape. hep-th/0507158
152. Firouzjahi H., and Tye S.H. The shape of gravity in a warped deformed conifold. JHEP 0601 (2006) 136. hep-th/0512076
153. Sen A. F-theory and orientifolds. Nucl. Phys. B 475 (1996) 562. hep-th/9605150
154. Dabholkar A., and Park J. Strings on orientifolds. Nucl. Phys. B 477 (1996) 701. hep-th/9604178
155. Becker K., Becker M., and Strominger A. Five-branes, membranes and nonperturbative string theory. Nucl. Phys. B 456 (1995) 130. hep-th/9507158
156. Marino M., Minasian R., Moore G.W., and Strominger A. Nonlinear instantons from supersymmetric p-branes. JHEP 0001 (2000) 005. hep-th/9911206
157. Bergshoeff E., Kallosh R., Ortin T., Roest D., and Van Proeyen A. New formulations of D = 10 supersymmetry and D8-O8 domain walls. Class. Quantum Grav. 18 (2001) 3359. hep-th/0103233
158. D'Auria R., and Ferrara S. Dyonic masses from conformal field strengths in D even dimensions. Phys. Lett. B 606 (2005) 211. hep-th/0410051
159. Louis J., and Schulgin W. Massive tensor multiplets in N = 1 supersymmetry. Fortschr. Phys. 53 (2005) 235. hep-th/0410149
160. Theis U. Masses and dualities in extended Freedman-Townsend models. Phys. Lett. B 609 (2005) 402. hep-th/0412177
161. Kuzenko S.M. On massive tensor multiplets. JHEP 0501 (2005) 041. hep-th/0412190
162. Binetruy P., Girardi G., and Grimm R. Supergravity couplings: A geometric formulation. Phys. Rep. 343 (2001) 255. hep-th/0005225
163. Wess J., and Bagger J. Supersymmetry and Supergravity (1992), Princeton Univ. Press, Princeton
164. Candelas P., and de la Ossa X. Moduli space of Calabi-Yau manifolds. Nucl. Phys. B 355 (1991) 455
165. Romans L.J. Massive N = 2 a supergravity in ten dimensions. Phys. Lett. B 169 (1986) 374
166. Jockers H., and Louis J. D-terms and F-terms from D7-brane fluxes. Nucl. Phys. B 718 (2005) 203. hep-th/0502059
167. Gukov S., Vafa C., and Witten E. CFT's from Calabi-Yau four-folds. Nucl. Phys. B 584 (2000) 69. hep-th/9906070
168. Gukov S., Vafa C., and Witten E. Nucl. Phys. B 608 (2001) 477 Erratum
169. Taylor T.R., and Vafa C. RR flux on Calabi-Yau and partial supersymmetry breaking. Phys. Lett. B 474 (2000) 130. hep-th/9912152
170. For a review see, for example, A. Klemm, Topological string theory on Calabi-Yau threefolds, PoS RTN2005 (2005) 002, and references therein
171. Cavalcanti G.R., and Gualtieri M. A surgery for generalized complex structures on 4-manifolds. math.DG/0602333
172. Van Proeyen A. Tools for supersymmetry. hep-th/9910030
173. 2, I/II. J. Diff. Geom. 43 (1996) 291
174. Beasley C., and Witten E. A note on fluxes and superpotentials in M-theory compactifications on manifolds of G(2) holonomy. JHEP 0207 (2002) 046. hep-th/0203061