T-duality with H-flux: Non-commutativity, T-folds and G × G structure

Nuclear Physics B

Volumn 770, Issue 1-2, 2007, Pages 123-144

  Grange, Pascal ^a   Schäfer Nameki, Sakura ^a,b  

^a UNIVERSITY OF HAMBURG   (Germany)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947727251     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2007.02.003     Document Type: Article

References (71)

1. Álvarez E., Álvarez-Gaumé L., Barbón J.L.F., and Lozano Y. Some global aspects of duality in string theory. Nucl. Phys. B 415 (1994) 71-100. hep-th/930903
2. Gurrieri S., Louis J., Micu A., and Waldram D. Mirror symmetry in generalized Calabi-Yau compactifications. Nucl. Phys. B 654 (2003) 61-113. hep-th/0211102
3. Kachru S., Schulz M.B., Tripathy P.K., and Trivedi S.P. New supersymmetric string compactifications. JHEP 0303 (2003) 061. hep-th/0211182
4. Hellerman S., McGreevy J., and Williams B. Geometric constructions of nongeometric string theories. JHEP 0401 (2004) 024. hep-th/0208174
5. Fidanza S., Minasian R., and Tomasiello A. Mirror symmetric SU (3)-structure manifolds with NS fluxes. Commun. Math. Phys. 254 (2005) 401-423. hep-th/0311122
6. Bouwknegt P., Evslin J., and Mathai V. T-duality: Topology change from H-flux. Commun. Math. Phys. 249 (2004) 383-415. hep-th/0306062
7. Mathai V., and Rosenberg J.M. On mysteriously missing T-duals, H-flux and the T-duality group. hep-th/0409073
8. Hull C.M. A geometry for non-geometric string backgrounds. JHEP 0510 (2005) 065. hep-th/0406102
9. Bouwknegt P., Hannabuss K., and Mathai V. Nonassociative tori and applications to T-duality. Commun. Math. Phys. 264 (2006) 41-69. hep-th/0412092
10. Shelton J., Taylor W., and Wecht B. Nongeometric flux compactifications. JHEP 0510 (2005) 085. hep-th/0508133
11. Ellwood I., and Hashimoto A. Effective descriptions of branes on non-geometric tori. hep-th/0607135
12. Mathai V., and Rosenberg J.M. T-duality for torus bundles via noncommutative topology. Commun. Math. Phys. 253 (2004) 705-721. hep-th/0401168
13. 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. Adv. Theor. Math. Phys. 10 (2006) 123-158. hep-th/0508084
14. Dabholkar A., and Hull C. Generalised T-duality and non-geometric backgrounds. JHEP 0605 (2006) 009. hep-th/0512005
15. Hull C.M. Doubled geometry and T-folds. hep-th/0605149
16. Hull C.M. Global aspects of T-duality, gauged sigma models and T-folds. hep-th/0604178
17. Lawrence A., Schulz M.B., and Wecht B. D-branes in nongeometric backgrounds. hep-th/0602025
18. Hellerman S., and Walcher J. Worldsheet CFTs for flat monodrofolds. hep-th/0604191
19. M. Graña, J. Louis, D. Waldram, in preparation
20. Hitchin N. Generalized Calabi-Yau manifolds. Quart. J. Math. Oxford Ser. 54 (2003) 281-308. math.DG/0209099
21. Gualtieri M. Generalized complex geometry. math.DG/0401221
22. Kapustin A. Topological strings on noncommutative manifolds. Int. J. Geom. Methods Mod. Phys. 1 (2004) 49-81. hep-th/0310057
23. Pestun V. Topological strings in generalized complex space. hep-th/0603145
24. Cattaneo A.S., and Felder G. A path integral approach to the Kontsevich quantization formula. Commun. Math. Phys. 212 (2000) 591-611. math.QA/9902090
25. Douglas M.R., and Hull C.M. D-branes and the noncommutative torus. JHEP 9802 (1998) 008. hep-th/9711165
26. Chu C.S., and Ho P.M. Noncommutative open string and D-brane. Nucl. Phys. B 550 (1999) 151. hep-th/9812219
27. Schomerus V. D-branes and deformation quantization. JHEP 9906 (1999) 030. hep-th/9903205
28. Seiberg N., and Witten E. String theory and noncommutative geometry. JHEP 9909 (1999) 032. hep-th/9908142
29. Anazawa M. D0-branes in a H-field background and noncommutative geometry. Nucl. Phys. B 569 (2000) 680-692. hep-th/9905055
30. Lowe D.A., Nastase H., and Ramgoolam S. Massive IIA string theory and matrix theory compactification. Nucl. Phys. B 667 (2003) 55-89. hep-th/0303173
31. Witten E. Overview of K-theory applied to strings. Int. J. Mod. Phys. A 16 (2001) 693-706. hep-th/0007175
32. Bouwknegt P., and Mathai V. D-branes, B-fields and twisted K-theory. JHEP 0003 (2000) 007. hep-th/0002023
33. Witten E. Noncommutative geometry and string field theory. Nucl. Phys. B 268 (1986) 253
34. Cavalcanti G., and Gualtieri M. Generalized complex structures in nilmanifolds. J. Symplectic Geom. 2 (2004) 393-410. math.DG/0404451
35. Graña M., Minasian R., Petrini M., and Tomasiello A. A scan for new N = 1 vacua on twisted tori. hep-th/0609124
36. Ooguri H., Oz Y., and Yin Z. D-branes on Calabi-Yau spaces and their mirrors. Nucl. Phys. B 477 (1996) 407-430. hep-th/9606112
37. Kapustin A., and Orlov D. Remarks on A-branes, mirror symmetry, and the Fukaya category. J. Geom. Phys. 48 (2003). hep-th/0109098
38. Chiantese S. Isotropic A-branes and the stability condition. JHEP 0502 (2005) 003. hep-th/0412181
39. Mariño M., Minasian R., Moore G.W., and Strominger A. Nonlinear instantons from supersymmetric p-branes. JHEP 0001 (2000) 005. hep-th/9911206
40. Kapustin A., and Li Y. Topological sigma-models with H-flux and twisted generalized complex manifolds. hep-th/0407249
41. Grange P., and Minasian R. Modified pure spinors and mirror symmetry. Nucl. Phys. B 732 (2006) 366-378. hep-th/0412086
42. Koerber P. Stable D-branes, calibrations and generalized Calabi-Yau geometry. JHEP 0508 (2005) 099. hep-th/0506154
43. Ben-Bassat O., and Boyarchenko M. Submanifolds of generalized complex manifolds. J. Symplectic Geom. 2 3 (2004) 309-355
44. Ben-Bassat O. Mirror symmetry and generalized complex manifolds. I. The transform on vector bundles, spinors, and branes. J. Geom. Phys. 56 4 (2006) 533-558
45. Martucci L., and Smyth P. Supersymmetric D-branes and calibrations on general N = 1 backgrounds. JHEP 0511 (2005) 048. hep-th/0507099
46. Martucci L. D-branes on general N = 1 backgrounds: Superpotentials and D-terms. JHEP 0606 (2006) 033. hep-th/0602129
47. Grange P., and Minasian R. Tachyon condensation and D-branes in generalized geometries. Nucl. Phys. B 741 (2006) 199-214. hep-th/0512185
48. Minasian R., and Moore G.W. K-theory and Ramond-Ramond charge. JHEP 9711 (1997) 002. hep-th/9710230
49. Witten E. D-branes and K-theory. JHEP 9812 (1998) 019. hep-th/9810188
50. Ben-Bassat O., Block J., and Pantev T. Non-commutative tori and Fourier-Mukai duality. math.AG/0509161
51. Witten E. A note on the antibracket formalism. Mod. Phys. Lett. A 5 (1990) 487
52. Ikeda N. Deformation of Batalin-Vilkovisky structures. math.SG/0604157
53. Schaller P., and Strobl T. Poisson structure induced (topological) field theories. Mod. Phys. Lett. A 9 (1994) 3129-3136. hep-th/9405110
54. Kontsevich M. Deformation quantization of Poisson manifolds. I. Lett. Math. Phys. 66 (2003) 157-216. hep-th/9709040
55. Cornalba L. D-brane physics and noncommutative Yang-Mills theory. Adv. Theor. Math. Phys. 4 (2000) 271-281. hep-th/9909081
56. Jurčo B., and Schupp P. Noncommutative Yang-Mills from equivalence of star products. Eur. Phys. J. C 14 (2000) 367-370. hep-th/0001032
57. Graña M., Minasian R., Petrini M., and Tomasiello A. Generalized structures of N = 1 vacua. JHEP 0511 (2005) 020. hep-th/0505212
58. Graña M., Louis J., and Waldram D. Hitchin functionals in N = 2 supergravity. JHEP 0601 (2006) 008. hep-th/0505264
59. Benmachiche I., and Grimm T.W. Generalized N = 1 orientifold compactifications and the Hitchin functionals. Nucl. Phys. B 748 (2006) 200-252. hep-th/0602241
60. Graña M. Flux compactifications in string theory: A comprehensive review. Phys. Rep. 423 (2006) 91-158. hep-th/0509003
61. Kapustin A., and Orlov D. Vertex algebras, mirror symmetry, and D-branes: The case of complex tori. Commun. Math. Phys. 233 (2003) 79-136. hep-th/0010293
62. Zucchini R. A sigma model field theoretic realization of Hitchin's generalized complex geometry. JHEP 0411 (2004) 045. hep-th/0409181
63. Zucchini R. Generalized complex geometry, generalized branes and the Hitchin sigma model. JHEP 0503 (2005) 022. hep-th/0501062
64. Howe P.S., Lindström U., and Stojevic V. Special holonomy sigma models with boundaries. JHEP 0601 (2006) 159. hep-th/0507035
65. Hassan S.F. O (d, d ; R) deformations of complex structures and extended world sheet supersymmetry. Nucl. Phys. B 454 (1995) 86-102. hep-th/9408060
66. Hassan S.F. T-duality, space-time spinors and RR fields in curved backgrounds. Nucl. Phys. B 568 (2000) 145-161. hep-th/9907152
67. Hassan S.F. SO (d, d) transformations of Ramond-Ramond fields and space-time spinors. Nucl. Phys. B 583 (2000) 431-453. hep-th/9912236
68. Lunin O., and Maldacena J.M. Deforming field theories with U (1) × U (1) global symmetry and their gravity duals. JHEP 0505 (2005) 033. hep-th/0502086
69. Minasian R., Petrini M., and Zaffaroni A. Gravity duals to deformed SYM theories and generalized complex geometry. hep-th/0606257
70. Strominger A., Yau S.-T., and Zaslow E. Mirror symmetry is T-duality. Nucl. Phys. B 479 (1996) 243-259. hep-th/9606040
71. Grange P. Branes as stable holomorphic line bundles on the non-commutative torus. JHEP 0410 (2004) 002. hep-th/0403126