Discrete torsion, non-abelian orbifolds and the Schur multiplier

Journal of High Energy Physics

Volumn 5, Issue 1, 2001, Pages

  Feng, Bo ^a   Hanany, Amihay ^a   He, Yang Hui ^a   Prezas, Nikolaos ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

AdS CFT Correspondance; Brane Dynamics in Gauge Theories; Discrete and Finite Symmetries; Non Commutative Geometry

Indexed keywords

EID: 33744833848     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2001/01/033     Document Type: Article

References (44)

1. A. Connes, M.R. Douglas and A. Schwarz, Noncommutative geometry and matrix theory: compactification on tori, J. High Energy Phys. 02 (1998) 003 [hep-th/9711162];
2. M.R. Douglas and C. Hull, D-branes and the noncommutative torus, J. High Energy Phys. 02 (1998) 008 [hep-th/9711165];
3. N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys. 09 (1999) 032 [hep-th/9908142].
4. C. Vafa, Modular invariance and discrete torsion on orbifolds, Nucl. Phys. B 273 (1986) 592.
5. C. Vafa and E. Witten, On orbifolds with discrete torsion, J. Geom. Phys. 15 (1995) 189 [hep-th/9409188].
6. M. Douglas, D-branes and discrete torsion, hep-th/9807235.
7. M.R. Douglas and B. Fiol, D-branes and discrete torsion, 2, hep-th/9903031.
8. M.R. Douglas and G. Moore, D-branes, quivers and ALE instantons, hep-th/9603167.
9. A. Lawrence, N. Nekrasov and C. Vafa, On conformal field theories in four dimensions, Nucl. Phys. B 533 (1998) 199 [hep-th/9803015].
10. D. Berenstein and R.G. Leigh, Discrete torsion, AdS/CFT and duality, J. High Energy Phys. 01 (2000) 038 [hep-th/0001055].
11. D. Berenstein, V. Jejjala and R.G. Leigh, Marginal and relevant deformations of N = 4 field theories and non-commutative moduli spaces of vacua, Nucl. Phys. B 589 (2000) 196 [hep-th/0005087];
12. Noncommutative moduli spaces and T-duality, Phys. Lett. B 493 (2000) 162 [hep-th/0006168];
13. D. Berenstein and R.G. Leigh, Non-commutative Calabi-Yau manifolds, hep-th/0009209.
14. S. Mukhopadhyay and K. Ray, D-branes on four folds with discrete torsion, Nucl. Phys. B 576 (2000) 152 [hep-th/9909107].
15. M. Klein and R. Rabadan, Orientifolds with discrete torsion, J. High Energy Phys. 07 (2000) 040 [hep-th/0002103];
16. M orientifolds with and without discrete torsion, J. High Energy Phys. 10 (2000) 049 [hep-th/0008173].
17. K. Dasgupta, S. Hyun, K. Oh and R. Tatar, Conifolds with discrete torsion and noncommutativity, J. High Energy Phys. 09 (2000) 043 [hep-th/0008091].
18. M.R. Gaberdiel, Discrete torsion orbifolds and D-branes, J. High Energy Phys. 11 (2000) 026 [hep-th/0008230].
19. E.R. Sharpe, Discrete torsion and gerbes, 1, hep-th/9909108;
20. Discrete torsion and gerbes, 2, hep-th/9909120;
21. Discrete torsion, hep-th/0008154;
22. Analogues of discrete torsion for the M-theory three-form, hep-th/0008170;
23. Discrete torsion in perturbative heterotic string theory, hep-th/0008184;
24. Recent developments in discrete torsion, hep-th/0008191.
25. Y.-H. He and J.S. Song, Of McKay correspondence, non-linear sigma-model and conformal field theory, hep-th/9903056.
26. J. Gomis, D-branes on orbifolds with discrete torsion and topological obstruction, J. High Energy Phys. 05 (2000) 006 [hep-th/0001200].
27. P.S. Aspinwall and M.R. Plesser, D-branes, discrete torsion and the McKay correspondence, hep-th/0009042.
28. P.S. Aspinwall, A note on the equivalence of Vafa's and Douglas's picture of discrete torsion, J. High Energy Phys. 12 (2000) 029 [hep-th/0009045].
29. A. Kapustin, D-branes in a topologically nontrivial B-field, hep-th/9909089.
30. G. Karpilovsky, Group representations, vol. II, Elsevier Science 1993.
31. G. Karpilovsky, Protective representations of finite groups, Pure and Applied Math. 1985.
32. G. Karpilovsky, The Schur multiplier, London Math. Soc. Monographs, New Series 2, Oxford 1987.
33. B. Feng, A. Hanany and Y.-H. He, Z-d brane box models and non-chiral dihedral quivers, hep-th/9909125.
34. The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.2, Aachen, St Andrews, 1999, http://www.math.rwth-aachen.de/̃GAP/WWW/gap.html.
35. D. Holt, The calculation of the Schur multiplier of a permutation group, M. Atkinsoned., Proc. Lond. Math. Soc. Meeting on Computational Group Theory, Durham 1982.
36. 3 and their applications to the elementary particle spectrum, J. Math. Physics 5, 8 (1964) 1038.
37. A. Hanany and Y.-H. He, Non-abelian finite gauge theories, J. High Energy Phys. 02 (1999) 013 [hep-th/9811183].
38. T. Muto, D-branes on three-dimensional nonabelian orbifolds, J. High Energy Phys. 02 (1999) 008 [hep-th/9811258].
39. A. Hanany and Y.-H. He, A monograph on the classification of the discrete subgroups of SU(4), hep-th/9905212.
40. C.V. Johnson and R.C. Myers, Aspects of type-IIB theory on ALE spaces, Phys. Rev. D 55 (1997) 6382 [hep-th/9610140].
41. S. Dulat and K. Wendland, Crystallographic orbifolds: towards a classification of unitary conformal field theories with central charge c = 2, J. High Energy Phys. 06 (2000) 012 [hep-th/0002227].
42. R. Dijkgraaf, Discrete torsion and symmetric products, hep-th/9912101;
43. P. Bantay, Symmetric products, permutation orbifolds and discrete torsion, hep-th/0004025.
44. D. Berenstein, private communications.