Non-commutative gauge theory of twisted D-branes

Nuclear Physics B

Volumn 646, Issue 3, 2002, Pages 127-157

  Alekseev, Anton Yu ^a,b   Fredenhagen, Stefan ^c   Quella, Thomas ^c   Schomerus, Volker ^c  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b UPPSALA UNIVERSITY   (Sweden)

^c ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Conformal field theory models in string theory; D branes; Non commutative geometry

Indexed keywords

EID: 0037121540     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0550-3213(02)00873-8     Document Type: Review

References (70)

1. I. Affleck, A.W.W. Ludwig, Critical theory of overscreened Kondo fixed points, Nucl. Phys. B 360 (1991) 641-696.
2. I. Affleck, A.W.W. Ludwig, The Kondo effect, conformal field theory and fusion rules, Nucl. Phys. B 352 (1991) 849-862.
3. I. Affleck, A.W.W. Ludwig, Universal noninteger 'ground state degeneracy' in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161-164.
4. A.Yu. Alekseev, V. Schomerus, RR Charges of D2-branes in the WZW Model, 2000.
5. A.Yu. Alekseev, A. Recknagel, V. Schomerus, Non-commutative world-volume geometries: branes on su(2) and fuzzy spheres, JHEP 09 (1999) 023.
6. A.Yu. Alekseev, A. Recknagel, V. Schomerus, Brane dynamics in background fluxes and non-commutative geometry, JHEP 05 (2000) 010.
7. A.Yu. Alekseev, A. Recknagel, V. Schomerus, Open strings and non-commutative geometry of branes on group manifolds, Mod. Phys. Lett. A 16 (2001) 325-336.
8. A.Yu. Alekseev, V. Schomerus, Representation theory of Chern-Simons observables, Duke Math. J. 85 (1996) 447-510.
9. A.Yu. Alekseev, V. Schomerus, D-branes in the WZW model, Phys. Rev. D 60 (1999) 061901.
10. C. Bachas, M.R. Douglas, C. Schweigert, Flux stabilization of D-branes, JHEP 05 (2000) 048.
11. R.E. Behrend, P.A. Pearce, V.B. Petkova, J.-B. Zuber, On the classification of bulk and boundary conformal field theories, Phys. Lett. B 444 (1998) 163-166.
12. R.E. Behrend, P.A. Pearce, V.B. Petkova, J.-B. Zuber, Boundary conditions in rational conformal field theories, Nucl. Phys. B 570 (2000) 525-589.
13. L. Birke, J. Fuchs, C. Schweigert, Symmetry breaking boundary conditions and WZW orbifolds, Adv. Theor. Math. Phys. 3 (1999) 671-726.
14. P. Bordalo, S. Ribault, C. Schweigert, Flux stabilization in compact groups, JHEP 10 (2001) 036.
15. P. Bouwknegt, V. Mathai, D-branes, B-fields and twisted K-theory, JHEP 03 (2000) 007.
16. J.L. Cardy, Boundary conditions, fusion rules and the Verlinde formula, Nucl. Phys. B 324 (1989) 581.
17. C.-S. Chu, P.-M. Ho, Noncommutative open string and D-brane, Nucl. Phys. B 550 (1999) 151-168.
18. A.M. Cohen, M. van Leeuwen, B. Lisser, LiE, 1996, this computer program can be obtained from http://young.sp2mi.univ-poitiers.fr/Οmarc/LiE/.
19. L. Cornalba, R. Schiappa, Nonassociative star product deformations for D-brane worldvolumes in curved backgrounds, Commun. Math. Phys. 225 (2002) 33-66.
20. P. Di Francesco, P. Mathieu, D. Senechal, Conformal Field Theory, in: Graduate Texts in Contemporary Physics, Springer, New York, 1999.
21. M.R. Douglas, C.M. Hull, D-branes and the noncommutative torus, JHEP 02 (1998) 008.
22. S. Elitzur, G. Sarkissian, D-branes on a gauged WZW model, Nucl. Phys. B 625 (2002) 166-178.
23. G. Felder, J. Fröhlich, J. Fuchs, C. Schweigert, Correlation Functions and Boundary Conditions in RCFT and Three-Dimensional Topology, 1999.
24. G. Felder, J. Fröhlich, J. Fuchs, C. Schweigert, Conformal boundary conditions and three-dimensional topological field theory, Phys. Rev. Lett. 84 (2000) 1659-1662.
25. G. Felder, J. Fröhlich, J. Fuchs, C. Schweigert, The geometry of WZW branes, J. Geom. Phys. 34 (2000) 162-190.
26. S. Fredenhagen, V. Schomerus, Brane Dynamics in CFT Backgrounds, 2001.
27. S. Fredenhagen, V. Schomerus, Branes on group manifolds, gluon condensates, and twisted K-theory, JHEP 04 (2001) 007.
28. S. Fredenhagen, V. Schomerus, D-branes in coset models, JHEP 02 (2002) 005.
29. J. Fröhlich, K. Gawedzki, Conformal Field Theory and Geometry of Strings, 1993.
30. J. Fröhlich, O. Grandjean, A. Recknagel, Supersymmetric Quantum Theory, Noncommutative Geometry, and Gravitation, 1995.
31. J. Fuchs, Affine Lie Algebras and Quantum Groups, in: Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press, Cambridge, 1995.
32. J. Fuchs, B. Schellekens, C. Schweigert, From Dynkin diagram symmetries to fixed point structures, Commun. Math. Phys. 180 (1996) 39-98.
33. J. Fuchs, C. Schweigert, Symmetry breaking boundaries I: General theory, Nucl. Phys. 419 (1999) 419-483.
34. W. Fulton, J. Harris, Representation Theory: A First Course, in: Graduate Texts in Mathematics, Vol. 129, Springer, 1991.
35. M.R. Gaberdiel, T. Gannon, Boundary states for WZW models, Nucl. Phys. 639 (2002) 471-501.
36. K. Gawedzki, Conformal Field Theory: a Case Study, 1999.
37. K. Gawedzki, Boundary WZW, G/H, G/G and CS Theories, 2001.
38. K. Hashimoto, K. Krasnov, D-brane solutions in non-commutative gauge theory on fuzzy sphere, Phys. Rev. 64 (2001) 046007.
39. K. Hayasaka, R. Nakayama, An associative and noncommutative product for the low energy effective theory of a D-brane in curved backgrounds and bi-local fields, Nucl. Phys. 624 (2002) 307-326.
40. Y. Hikida, M. Nozaki, Y. Sugawara, Formation of spherical D2-brane from multiple D0-branes, Nucl. Phys. B 617 (2001) 117-150.
41. J. Hoppe, Diffeomorphism groups, quantization and su(infinity), Int. J. Mod. Phys. A 4 (1989) 5235.
42. D. Husemoller, Fibre Bundles, in: Graduate Texts in Mathematics, Vol. 20, 3rd Edition, Springer, 1994.
43. V.G. Kac, Infinite Dimensional Lie Algebras, Cambridge Univ. Press, Cambridge, 1990.
44. A. Klimyk, Multiplicities of weights of representations and multiplicities of representations of semisimple Lie algebras, Soviet Math. Dokl. 89 (1967) 1531-1534, published originally in Dokl. Akad. Nauk SSSR 177 (5) (1967) 1001-1004, in Russian.
45. D.C. Lewellen, Sewing constraints for conformal field theories on surfaces with boundaries, Nucl. Phys. B 372 (1992) 654-682.
46. J. Madore, The fuzzy sphere, Class. Quantum Grav. 9 (1992) 69-88.
47. J.M. Maldacena, G.W. Moore, N. Seiberg, D-brane instantons and K-theory charges, JHEP 11 (2001) 062.
48. J.M. Maldacena, G.W. Moore, N. Seiberg, Geometrical interpretation of D-branes in gauged WZW models, JHEP 07 (2001) 046.
49. W.G. McKay, J. Patera, Tables of Dimensions, Indices, and Branching Rules for Representations of Simple Lie Algebras, Dekker, New York, 1981.
50. W.G. McKay, J. Patera, D.W. Rand, in: Tables of Representations of Simple Lie Algebras, Vol. I, Centre de Recherches Mathematiques, Montreal, 1990.
51. R.V. Moody, J. Patera, D.W. Rand. SimpLie, 2000, this computer program can be obtained from http://omega.CRM.UMontreal.CA/Οrand/simpLie.html.
52. R.C. Myers, Dielectric-branes, JHEP 12 (1999) 022.
53. J. Pawelczyk, SU(2) WZW D-branes and their noncommutative geometry from DBI action, JHEP 08 (2000) 006.
54. J. Pawelczyk, H. Steinacker, A Quantum Algebraic Description of D-branes on Group Manifolds, 2002.
55. V.B. Petkova, J.B. Zuber, Boundary Conditions in Charge Conjugate sl(n) WZW Theories, 2002.
56. G. Pradisi, A. Sagnotti, Ya.S. Stanev, Completeness conditions for boundary operators in 2D conformal field theory, Phys. Lett. B 381 (1996) 97-104.
57. T. Quella, Branching rules of semi-simple Lie algebras using affine extensions, J. Phys. A 35 (2002) 3743-3754.
58. T. Quella, I. Runkel, C. Schweigert, An Algorithm for Twisted Fusion Rules, 2002.
59. T. Quella, V. Schomerus, Symmetry breaking boundary states and defect lines, JHEP 06 (2002) 028.
60. A. Recknagel, V. Schomerus, D-branes in Gepner models, Nucl. Phys. B 531 (1998) 185-225.
61. A. Recknagel, V. Schomerus, Boundary deformation theory and moduli spaces of D-branes, Nucl. Phys. B 545 (1999) 233-282.
62. A. Recknagel, V. Schomerus, Moduli spaces of D-branes in CFT-backgrounds, Nucl. Phys. B 48 (2000) 195-198.
63. I. Runkel, Boundary structure constants for the A-series Virasoro minimal models, Nucl. Phys. B 549 (1999) 563-578.
64. I. Runkel, Structure constants for the D-series Virasoro minimal models, Nucl. Phys. B 579 (2000) 561-589.
65. V. Schomerus, D-branes and deformation quantization, JHEP 06 (1999) 030.
66. N. Seiberg, E.Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032.
67. S. Stanciu, D-branes in Kazama-Suzuki models, Nucl. Phys. B 526 (1998) 295-310.
68. S. Stanciu, D-branes in group manifolds, JHEP 01 (2000) 025.
69. S. Stanciu, An Illustrated Guide to D-branes in su(3), 2001.
70. E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nucl. Phys. B 300 (1988) 360.