Abelian and non-Abelian branes in WZW models and gerbes

Communications in Mathematical Physics

Volumn 258, Issue 1, 2005, Pages 23-73

  Gawedzki, Krzysztof ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 20644441585     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1301-1     Document Type: Article

References (76)

1. Alekseev, A., Meinrenken, E., Woodward, C.: The Verlinde formulas as fixed point formulas. J. Symplectic Geom. 1, 1-46 (2001)
2. Alekseev, A., Meinrenken, E., Woodward, C.: The Verlinde formulas as fixed point formulas. J. Symplectic Geom. and 1, 427-434 (2002)
3. Alekseev, A. Yu., Schomerus, V.: D-branes in the WZW model. Phys. Rev. D 60, R061901-R061902 (1999)
4. Alvarez, O.: Topological quantization and cohomology. Commun. Math. Phys. 100, 279-309 (1985)
5. Alvarez-Gaumé, L., Gomez, C., Sierra, G.: Quantum group interpretation of some conformal field theories. Phys. Lett. B 220, 142-152 (1989)
6. Aspinwall, P. S.: D-branes on Calabi-Yau manifolds, http://arxiv.org/abs/list/hep-th/0403166, 2004
7. Bachas, C., Douglas, M. Schweigert, C.: Flux stabilization of D-branes. JHEP 05, 048 (2000)
8. Behrend, R. E., Pearce, P. A., Petkova, V. B., Zuber, J.-B.: Boundary conditions in rational conformal field theories. Nucl. Phys. B 579, 707-773 (2000)
9. Behrend, K., Xu, P. Zhang, B.: Equivariant gerbes over compact simple Lie groups. C. R. Acad. Sci. Paris 336 Sér. 1, 251-256 (2003)
10. Birke, L., Fuchs, J., Schweigert, C.: Symmetry breaking boundary conditions and WZW orbifolds. Adv. Theor. Math. Phys. 3, 671-726 (1999)
11. Bouwknegt, P., Carey, A. L., Mathai, V., Murray, M. K., Stevenson, D.: Twisted K-theory and K-theory of bundle gerbes. Commun. Math. Phys. 228, 17-45 (2002)
12. Bouwknegt, P., Dawson, P., Ridout, D.: D-branes on group manifolds and fusion rings. JHEP 12, 065 (2002)
13. Bouwknegt, P., Ridout, D.: A note on the equality of algebraic and geometric D-brane charges in WZW models. JHEP 05, 029 (2004)
14. Braun, V.: Twisted K-theory of Lie groups. JHEP 03, 029 (2004)
15. Braun, V., Schafer-Nameki, S.: Supersymmetric WZW models and twisted K-theory of SO(3). http://arxiv.org/abs/hep-th/0403287, 2004
16. Bruner, I., Schomerus, V.: On Superpotentials for D-branes in Gepner models. JHEP 10, 016 (2000)
17. Brylinski, J.-L.: Loop Spaces, Characteristic Classes and Geometric Quantization. Prog. Math. 107, Boston: Birkhäuser, 1993
18. Brylinski, J.-L.: Gerbes on complex reductive Lie groups. http://arxiv/org/list/math.DG/0002158, 2000
19. Cardy, J. L.: Boundary conditions, fusion rules and the Verlinde formula. Nucl. Phys. B 324, 581-598 (1989)
20. Carey, A. L., Johnson, S., Murray, M. K.: Holonomy on D-Branes. http://arxiv.org/list/hep-th/0204199, 2002
21. Carter, J. S., Flath, D. E., Saito, M.: The Classical and Quantum 6j-Symbols. Princeton, NJ: Princeton U. Press, 1995
22. Chatterjee, D. S.: On gerbs. Ph.D. thesis, Trinity College, Cambridge, 1998
23. Di Francesco, P., Mathieu, P., Sénéchal, D.: Conformal Field Theory. New York: Springer-Verlag, 1997
24. Douglas, M.: D-branes and discrete torsion. http://arxiv.org/list/hep-th/9807235, 1998
25. Douglas, M.: Topics in D-geometry. Class. Quant. Grav. 17, 1057-1070 (2000)
26. Douglas, M.: Lectures on D-branes on Calabi-Yau manifolds. ICTP Lect. Notes, VII, Trieste 2002, http://www.ictp.trieste.it/~pub_off/lectures/vol7.html
27. Douglas, M., Fiol, B.: D-branes and discrete torsion II. http://arxiv.org/list/hep-th/9903031, 1999
28. Felder, G., Fröhlich, J., Fuchs, J., Schweigert, C.: Conformal boundary conditions and three-dimensional topological field theory. Phys. Rev. Lett. 84, 1659-1662 (2000)
29. Elitzur, S., Sarkissian, G.: D-Branes on a gauged WZW model. Nucl.Phys. B 625, 166-178 (2002)
30. Felder, G., Gawȩdzki, K., Kupiainen, A.: Spectra of Wess-Zumino-Witten models with arbitrary simple groups. Commun. Math. Phys. 117, 127-158 (1988)
31. Fredenhagen, S., Schomerus, V.: Branes on group manifolds, gluon condensates, and twisted K-theory. JHEP 04, 007 (2001)
32. Freed, D. S., Witten, E.: Anomalies in string theory with D-branes. Asian J. Math. 3, 819-851 (1999)
33. Fuchs, J., Huiszoon, L. R., Schellekens, A. N., Schweigert, C., Walcher, J.: Boundaries, crosscaps and simple currents. Phys. Lett. B 495, 421-434 (2000)
34. Fuchs, J., Kaste, P., Lerche, W., Lutken, C., Schweigert, C., Walcher, J: Boundary fixed points, enhanced Gauge symmetry and singular bundles on K3. Nucl. Phys. B598, 57-72 (2001)
35. Fuchs, J., Runkel, I., Schweigert, C.: TFT construction of RCFT correlators III: Simple currents. Nucl. Phys. B694, 277-353 (2004)
36. Fuchs, J., Schweigert, C.: The action of outer automorphisms on bundles of chiral blocks. Commun. Math. Phys. 206, 691-736 (1999)
37. Gaberdiel, M. R., Gannon, T.: Boundary states for WZW models. Nucl. Phys. B 639, 471-501 (2002)
38. Gaberdiel, M. R., Gannon, T.: D-brane charges on non-simply connected groups. JHEP 04, 030 (2004)
39. K. Gawȩdzki, Topological actions in two-dimensional quantum field theories. In: Non-perturbative Quantum Field Theory, eds. 't Hooft, G., Jaffe, A., Mack, G., Mitter, P. K., Stora, R., New York: Plenum Press, 1988, pp. 101-142
40. Gawȩdzki, K.: Conformal field theory: a case study. In: Conformal Field Theory: New Non-Perturbative Methods in String and Field Theory, eds. Nutku, Y., Saclioglu, C., Turgut, T., London: Perseus, 2000, pp. 1-55
41. Gawȩdzki, K.: Boundary WZW, G/H, G/G and CS theories. Ann. Henri Poincaré 3, 847-881 (2002)
42. Gawédzki, K., Reis, N.: WZW branes and gerbes. Rev. Math. Phys. 14, 1281-1334 (2002)
43. Gawédzki, K., Reis, N.: Basic gerbe over non-simply connected compact groups. J. Geom. Phys. 50, 28-55 (2004)
44. Gawédzki, K., Todorov, I., Tran-Ngoc-Bich, P.: Canonical quantization of the boundary Wess-Zumino-Witten model. Commun. Math. Phys: 248, 217-254 (2004)
45. Gepner, D., E. Witten, E.: String Theory on Group Manifolds. Nucl. Phys. B 278, 493-549 (1986)
46. Giraud, J.: Cohomologie non-abélienne. Grundl. 179, Berlin-Heidelberg-New York: Springer, 1971
47. Halpern, M. B., Helfgott, C.: The general twisted open WZW string, http://arxiv.org/list/hep-th/0406003, 2004 and references therein
48. Hitchin, N. J.: Lectures on special Lagrangian submanifolds. In: Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifold, eds. Vafa, C., Yau, S.-T., AMS/IP Stud. Adv. Math. Vol. 23, Providence, RI: Amer. Math. Soc., 2001, pp. 151-182
49. Kac, V. G.: Infinite Dimensional Lie Algebras. Cambridge: Cambridge University Press, 1985
50. Kapustin, A.: D-branes in a topologically nontrivial B-field. Adv. Theor. Math. Phys. 4, 127-154 (2000)
51. Klimčik, C., Ševera, P.: Open Strings and D-branes in WZNW model. Nucl. Phys. B488, 653-676 (1997)
52. Kontsevich, M.: Mirror symmetry in dimension 3. Séminaire Bourbaki, 801, Astérisque 237, 275-293 (1996)
53. B. Kostant: Quantization and unitary representations. Lecture Notes in Math., Vol. 170, Berlin: Springer, 1970, pp. 87-207
54. Kreuzer, M, Schellekens, A., N.: Simple currents versus orbifolds with discrete torsion - a complete classification. Nucl. Phys. B 411, 97-121 (1994)
55. Mackaay, M.: A note on the holonomy of connections in twisted bundles. http://arxiv.org/list/math.DG/0106019, 2001
56. Matsubara, K., Schomerus, V., Smedback, M.: Open strings in simple current orbifolds. Nucl. Phys. B O626, 53-72 (2002)
57. Meinrenken, E.: The basic gerbe over a compact simple Lie group. L'Enseignement Mathematique 49, 307-333 (2003)
58. Moore, G.: K-Theory from a physical perspective. http://arxiv.org/list/hep-th/0304018, 2003
59. Moore, G., Seiberg, N.: Lectures on RCFT. Physics, Geometry, and Topology, New York: Plenum Press, 1990
60. Murray, M. K.: Bundle gerbes. J. London Math. Soc. (2) 54, 403-416 (1996)
61. Murray, M. K., Stevenson, D.: Bundle gerbes: stable isomorphisms and local theory. J. London Math. Soc. (2) 62, 925-937 (2000)
62. Pawe Iczyk, J.: SU(2) WZW D-branes and their non-commutative geometry from DBI action. JHEP 08, 006 (2000)
63. Petkova, V. B., Zuber, J.-B.: Conformal boundary conditions and what they teach us. In: Proceedings of Nonperturbative Quantum Field Theoretic Methods and their Applications, Horvath, Z., Palla, L. eds., Singapore: World Scientific, 2001, pp. 1-35
64. Picken, R.: TQFT's and gerbes. In: Algebraic and Geometric Topology 4, 243-272 (2004)
65. Polchinski, J.: TASI lectures on D-branes. http://arxiv.org/list/hep-th/9611050, 1996
66. Reis, N.: Geometric interpretation of boundary conformal field theories. Ph.D. thesis. ENS-Lyon 2003
67. Runkel, I.: Boundary structure constants for the A-series Virasoro minimal models. Nucl. Phys. B 549, 563-578 (1999)
68. Runkel, I.: Structure constants for the D-series Virasoro minimal models. Nucl. Phys. B 579, 561-589 (2000)
69. Schellekens, A. N.: The program Kac. http://www.nikhef.nl/~t58/kac, 1996
70. Schweigen, C., Fuchs, J., Walcher, J.: Conformal field theory, boundary conditions and applications to string theory. In: Non-Perturbative QFT Methods and Their Applications, Horvath, Z., Palla, L. eds., Singapore: World Scientific, 2001, pp. 37-93
71. Schomerus, V.: Lectures on branes in curved backgrounds. Class. Quant. Grav. 19, 5781-5847 (2002)
72. Sharpe, E. R.: Discrete torsion and gerbes I, II. http://arxiv.org/list/hep-th/9909108, and http://arxiv.org/list/hep-th/9909120, 1999
73. Vafa, C.: Modular invariance and discrete torsion on orbifolds. Nucl. Phys. B 273, 592-606 (1986)
74. Walcher, J.: Worldsheet boundaries, supersymmetry, and quantum geometry. ETH dissertation No. 14225, 2001
75. Witten, E.: Non-abelian bosonization in two dimensions. Commun. Math. Phys. 92, 455-472 (1984)
76. Witten, E.: Overview of K-theory applied to strings. J. Mod. Phys. A16, 693-706 (2001)