Notes on orientifolds of rational conformal field theories

Journal of High Energy Physics

Volumn 8, Issue 7, 2004, Pages 505-563

  Brunner, Ilka ^a   Hori, Kentaro ^b,c  

^a CERN   (Switzerland)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Conformal and W Symmetry; Conformal Field Models in String Theory; D branes

Indexed keywords

EID: 23044443056     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2004/07/023     Document Type: Article

References (73)

1. A. Sagnotti, Open strings and their symmetry groups, talk presented at the Cargèse summer institute on non-perturbative methods infield theory, Cargèse, 1987 [hep-th/0208020].
2. M. Bianchi and A. Sagnotti, On the systematics of open string theories, Phys. Lett. B 247 (1990) 517.
3. M. Bianchi and A. Sagnotti, Twist symmetry and open string Wilson lines, Nucl. Phys. B 361 (1991) 519.
4. P. Hořava, Strings on world sheet orbifolds, Nucl. Phys. B 327 (1989) 461.
5. P. Hořava, Background duality of open string models, Phys. Lett. B 231 (1989) 251.
6. C. Angelantonj and A. Sagnotti, Open strings, Phys. Rept. 371 (2002) 1 [hep-th/0204089].
7. C.G. Callan Jr., C. Lovelace, C.R. Nappi and S.A. Yost, Adding holes and crosscaps to the superstring, Nucl. Phys. B 293 (1987) 83.
8. J. Polchinski and Y. Cai, Consistency of open superstring theories, Nucl. Phys. B 296 (1988) 91.
9. E.G. Gimon and J. Polchinski, Consistency conditions for orientifolds and D-manifolds, Phys. Rev. D 54 (1996) 1667 [hep-th/9601038].
10. G. Pradisi and A. Sagnotti, Open string orbifolds, Phys. Lett. B 216 (1989) 59.
11. C. Vafa and E. Witten, Dual string pairs with N = 1 and N = 2 supersymmetry in four dimensions, Nucl. Phys. 46 (Proc. Suppl.) (1996) 225 [hep-th/9507050];
12. C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y.S. Stanev, Chiral asymmetry in four-dimensional open-string vacua, Phys. Lett. B 385 (1996) 96 [hep-th/9606169];
13. M. Berkooz and R.G. Leigh, A D = 4 N = 1 orbifold of type-I strings, Nucl. Phys. B 483 (1997) 187 [hep-th/9605049];
14. Z. Kakushadze and G. Shiu, A chiral N = 1 type-I vacuum in four dimensions and its heterotic dual, Phys. Rev. D 56 (1997) 3686 [hep-th/9705163];
15. Z. Kakushadze and G. Shiu, 4d chiral N = 1 type-I vacua with and without D5-branes, Nucl. Phys. B 520 (1998) 75 [hep-th/9706051];
16. M orientifolds, Nucl. Phys. B 526 (1998) 378 [hep-th/9708040];
17. G. Aldazabal, A. Font, L.E. Ibáñez and G. Violero, D = 4, N = 1, type-IIB orientifolds, Nucl. Phys. B 536 (1998) 29 [hep-th/9804026];
18. R. Blumenhagen, L. Görlich and B. Körs, Supersymmetric 4d orientifolds of type-IIA with D6-branes at angles, J. High Energy Phys. 01 (2000) 040 [hep-th/9912204];
19. R. Blumenhagen, L. Görlich, B. Körs and D. Lüst, Noncommutative compactifications of type-I strings on tori with magnetic background flux, J. High Energy Phys. 10 (2000) 006 [hep-th/0007024];
20. M orientifolds in 4d with D-branes at angles, Nucl. Phys. B 593 (2001) 127 [hep-th/0008250];
21. 6 orientifold, Nucl. Phys. B 595 (2001) 63 [hep-th/0010091];
22. 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];
23. S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097];
24. S. Kachru, M.B. Schulz and S. Trivedi, Moduli stabilization from fluxes in a simple IIB orientifold, J. High Energy Phys. 10 (2003) 007 [hep-th/0201028].
25. R. Blumenhagen and A. Wisskirchen, Spectra of 4d, N = 1 type-I string vacua on non-toroidal CY threefolds, Phys. Lett. B 438 (1998) 52 [hep-th/9806131].
26. C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y.S. Stanev, Comments on gepner models and type-I vacua in string theory, Phys. Lett. B 387 (1996) 743 [hep-th/9607229].
27. I. Brunner and K. Hori, to appear.
28. G. Pradisi, A. Sagnotti and Y.S. Stanev, Planar duality in SU(2) WZW models, Phys. Lett. B 354 (1995) 279 [hep-th/9503207].
29. L.R. Huiszoon, A.N. Schellekens and N. Sousa, Klein bottles and simple currents, Phys. Lett. B 470 (1999) 95 [hep-th/9909114].
30. J. Fuchs, L.R. Huiszoon, A.N. Schellekens, C. Schweigert and J. Walcher, Boundaries, crosscaps and simple currents, Phys. Lett. B 495 (2000) 427 [hep-th/0007174].
31. L.R. Huiszoon and A.N. Schellekens, Crosscaps, boundaries and T-duality, Nucl. Phys. B 584 (2000) 705 [hep-th/0004100].
32. L.R. Huiszoon, A.N. Schellekens and N. Sousa, Open descendants of non-diagonal invariants, Nucl. Phys. B 575 (2000) 401 [hep-th/9911229].
33. H. Ooguri, Y. Oz and Z. Yin, D-branes on Calabi-Yau spaces and their mirrors, Nucl. Phys. B 477 (1996) 407 [hep-th/9606112].
34. J.M. Maldacena, G.W. Moore and N. Seiberg, Geometrical interpretation of D-branes in gauged WZW models, J. High Energy Phys. 07 (2001) 046 [hep-th/0105038].
35. Y. Hikida, Orientifolds of SU(2)/U(1) WZW models, J. High Energy Phys. 11 (2002) 035 [hep-th/0201175].
36. J.L. Cardy, Boundary conditions, fusion rules and the Verlinde formula, Nucl. Phys. B 324 (1989) 581.
37. N. Ishibashi, The boundary and crosscap states in conformal field theories, Mod. Phys. Lett. A 4 (1989) 251.
38. G. Pradisi, A. Sagnotti and Y.S. Stanev, The open descendants of nondiagonal SU(2) WZW models, Phys. Lett. B 356 (1995) 230 [hep-th/9506014].
39. P. Bantay, The frobenius-schur indicator in conformal field theory, Phys. Lett. B 394 (1997) 87 [hep-th/9610192].
40. P. Bantay, Frobenius-schur indicators, the Klein-bottle amplitude and the principle of orbifold covariance, Phys. Lett. B 488 (2000) 207 [hep-th/0001173].
41. J. Fuchs and C. Schweigert, Branes: from free fields to general backgrounds, Nucl. Phys. B 530 (1998) 99 [hep-th/9712257].
42. E. Verlinde, Fusion rules and modular transformations in 2-d conformal field theory, Nucl. Phys. B 300 (1988) 360.
43. J. Fuchs and C. Schweigert, Symmetry breaking boundaries, I. General theory, Nucl. Phys. B 558 (1999) 419 [hep-th/9902132].
44. J. Fuchs and C. Schweigert, Symmetry breaking boundaries, II. More structures, examples, Nucl. Phys. B 568 (2000) 543 [hep-th/9908025].
45. L. Birke, J. Fuchs and C. Schweigert, Symmetry breaking boundary conditions and WZW orbifolds, Adv. Theor. Math. Phys. 3 (1999) 671 [hep-th/9905038].
46. C. Vafa, Modular invariance and discrete torsion on orbifolds, Nucl. Phys. B 273 (1986) 592.
47. G. Karpilovsky, Protective representations of finite groups, Monographs and textbooks in pure and applied mathematics 94 Marcel Dekker, 1985.
48. M. Green, J. Schwarz and E. Witten, Superstring theory, Cambridge University Press, Cambridge 1987.
49. A. Sen and S. Sethi, The mirror transform of type-I vacua in six dimensions, Nucl. Phys. B 499 (1997) 45 [hep-th/9703157].
50. C. Angelantonj, I. Antoniadis, G. D'Appollonio, E. Dudas and A. Sagnotti, Type I vacua with brane supersymmetry breaking, Nucl. Phys. B 572 (2000) 36 [hep-th/9911081].
51. M. Klein and R. Rabadán, Orientifolds with discrete torsion, J. High Energy Phys. 07 (2000) 040 [hep-th/0002103].
52. A. Recknagel and V. Schomerus, D-branes in Gepner models, Nucl. Phys. B 531 (1998) 185 [hep-th/9712186].
53. B. Acharya, M. Aganagic, K. Hori and C. Vafa, Orientifolds, mirror symmetry and superpotentials, hep-th/0202208.
54. E. Witten, Toroidal compactification without vector structure, J. High Energy Phys. 02 (1998) 006 [hep-th/9712028].
55. E. Witten, Nonabelian bosonization in two dimensions, Commun. Math. Phys. 92 (1984) 455.
56. A.M. Polyakov and P.B. Wiegmann, Goldstone fields in two-dimensions with multivalued actions, Phys. Lett. B 141 (1984) 223.
57. K. Gawȩdzki and A. Kupiainen, Coset construction from functional integrals, Nucl. Phys. B 320 (1989) 625.
58. K. Hori, Global aspects of gauged Wess-Zumino-Witten models, Commun. Math. Phys. 182 (1996) 1 [hep-th/9411134].
59. P. Hořava, Chern-Simons gauge theory on orbifolds: open strings from three dimensions, J. Geom. Phys. 21 (1996) 1 [hep-th/9404101].
60. M. Bianchi and Y.S. Stanev, Open strings on the Neveu-Schwarz pentabrane, Nucl. Phys. B 523 (1998) 193 [hep-th/9711069].
61. A.Y. Alekseev and V. Schomerus, D-branes in the WZW model, Phys. Rev. D 60 (1999) 061901 [hep-th/9812193].
62. A.Y. Alekseev, A. Recknagel and V. Schomerus, Non-commutative world-volume geometries: branes on SU(2) and fuzzy spheres, J. High Energy Phys. 09 (1999) 023 [hep-th/9908040].
63. G. Felder, J. Fröhlich, J. Fuchs and C. Schweigert, The geometry of WZW branes, J. Geom. Phys. 34 (2000) 162 [hep-th/9909030].
64. I. Brunner, On orientifolds of WZW models and their relation to geometry, J. High Energy Phys. 01 (2002) 007 [hep-th/0110219].
65. L.R. Huiszoon, K. Schalm and A.N. Schellekens, Geometry of WZW orientifolds, Nucl. Phys. B 624 (2002) 219 [hep-th/0110267].
66. C. Bachas, N. Couchoud and P. Windey, Orientifolds of the 3-sphere, J. High Energy Phys. 12 (2001) 003 [hep-th/0111002].
67. R.E. Behrend, P.A. Pearce, V.B. Petkova and J.-B. Zuber, Boundary conditions in rational conformal field theories, Nucl. Phys. B 570 (2000) 525
68. Nucl. Phys. B 579 (2000) 707 [hep-th/9908036].
69. R. Dijkgraaf and E. Verlinde, Modular invariance and the fusion algebra, Nucl. Phys. 5B (Proc. Suppl.) (1988) 87.
70. A.N. Schellekens and S. Yankielowicz, Extended chiral algebras and modular invariant partition functions, Nucl. Phys. B 327 (1989) 673.
71. A.N. Schellekens and S. Yankielowicz, Modular invariants from simple currents: an explicit proof, Phys. Lett. B 227 (1989) 387.
72. K.A. Intriligator, Bonus symmetry in conformal field theory, Nucl. Phys. B 332 (1990) 541.
73. M. Kreuzer and A.N. Schellekens, Simple currents versus orbifolds with discrete torsion: a complete classification, Nucl. Phys. B 411 (1994) 97 [hep-th/9306145].