NC branes and hierarchies in quantum Hall fluids

Journal of High Energy Physics

Volumn 6, Issue 5, 2002, Pages 53-75

  Rhalami, Aziz El ^a   Sahraoui, El Mostapha ^a   Saidi, El Hassan ^a  

^a FACULTÉ DES SCIENCES   (Morocco)

Author keywords

D branes; Field Theories in Lower Dimensions; M(atrix) Theories; Superstring Vacua

Indexed keywords

EID: 23044493016     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2002/05/004     Document Type: Article

References (44)

1. L. Susskind, The quantum Hall fluid and non-commutative Chern-Simons theory, hep-th/0101029.
2. C. Duval and P.A. Horvathy, Exotic galilean symmetry in the non-commutative plane and the Hall effect, J. Phys. A 34 (2001) 10097 [hep-th/0106089].
3. B. Morariu and A.P. Polychronakos, Finite noncommutative Chern-Simons with a Wilson Une and the quantum Hall effect, J. High Energy Phys. 07 (2001) 006 [hep-th/0106072].
4. A.P. Polychronakos, Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory, J. High Energy Phys. 06 (2001) 070 [hep-th/0106011].
5. S. Hellerman and M. Van Raamsdonk, Quantum Hall physics equals noncommutative field theory, J. High Energy Phys. 10 (2001) 039 [hep-th/0103179].
6. D. Bak, S.K. Kim, K.-S. Soh, J.H. Yee, Noncommutative Chern-Simons solitons, Phys. Rev. D 64 (2001) 025018 [hep-th/0102137].
7. J.H. Brodie, L. Susskind and N. Toumbas, How Bob Laughlin tamed the giant graviton from Taub-NUT space, J. High Energy Phys. 02 (2001) 003 [hep-th/0010105].
8. S.S. Gubser and M. Rangamani, D-brane dynamics and the quantum Hall effect, J. High Energy Phys. 05 (2001) 041 [hep-th/0012155].
9. S. Hellerman and L. Susskind, Realizing the quantum Hall system in string theory, hep-th/0107200.
10. O. Bergman, Y. Okawa and J.H. Brodie, The stringy quantum Hall fluid, J. High Energy Phys. 11 (2001) 019 [hep-th/0107178].
11. A. Khare, M.B. Paranjape, J. High Energy Phys. 04 (2001) 002.
12. R.B. Laughlin, Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50 (1983) 1395;
13. E. Fradkin, Field theories of condensed matter systems, Lecture Note Series 82 1991.
14. X.G. Wen and A. Zee, Classification of abelian quantum Hall states and matrix formulation of topological fluids, Phys. Rev. B 46 (1992) 2290;
15. X.-G. Wen, Topological orders and edge excitations in FQH states, cond-mat/9506066.
16. R.B. Laughlin, Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50 (1983) 1395;
17. D. Arovas, J.R. Schrieffer and F. Wilczek, Fractional statistics and the quantum Hall effect, Phys. Rev. Lett. 53 (1984) 722.
18. S. Bahcall and L. Susskind, Fluid dynamics, Chern-Simons theory and the quantum Hall effect, Int. J. Mod. Phys. B 5 (1991) 2735.
19. X.G. Wen and A. Zee, Classification of abelian quantum Hall states and matrix formulation of topological fluids, Phys. Rev. B 46 (1992) 2290;
20. B. Blok and X.G. Wen, The structure of the microscopic theory of the hierarchical fractional quantum Hall effect, Phys. Rev. B 43 (1991) 8337;
21. Effective theories of fractional quantum Hall effect: the hierarchy construction, Phys. Rev. B 42 (1990) 8145;
22. Effective theories of fractional quantum Hall effect at generic filling fractions, Phys. Rev. B 42 (1990) 8133;
23. A. Jellal, Fractional quantum Hall effect and (2 + 1)-dimensional quantum electrodynamics, Int. J. Theor. Phys. 37 (1998) 2751.
24. J. Fröhlich and A. Zee, Large scale physics of the quantum Hall fluid, Nucl. Phys. B 364 (1991) 517;
25. J. Fröhlich, T. Kerler and E. Thiran, Structure the set of incompressible quantum Hall fluids, Nucl. Phys. B 453 (1995) 670.
26. N. Read, Excitation structure of the hierarchy scheme in the fractional quantum Hall effect, Phys. Rev. Lett. 65 (1990) 1502.
27. B. Blok and X.G. Wen, Effective theories of fractional quantum Hall effect at generic filling fractions, Phys. Rev. B 42 (1990) 8133.
28. R.E. Prange and S.M. Girvin, The quantum Hall effect, Springer, New York 1987.
29. F.D.M. Haldane, Fractional quantization of the Hall effect: a hierarchy of incompressible quantum fluid states, Phys. Rev. Lett. 51 (1983) 605.
30. E. Fradkin, Field theories of condensed matter systems, Addison Wesley, Redwood City 1991.
31. S.M. Girvin, The quantum Hall effect: novel excitations and broken symmetries, cond-mat/9907002.
32. S. Hellerman and L. Susskind, Realizing the quantum Hall system in string theory, hep-th/0107200.
33. I. Benkaddour, A. El Ehalami and E.H. Saidi, Fractional quantum Hall excitations as rdts highest weight state representations, hep-th/0101188.
34. A. Zee, Quantum Hall fluid, in Field theory, topology and condensed matter physics, proceedings of the Ninth Chris Engelbrecht summer school in theoretical physics, Storms River Mouth, Tsitsikamma National Park, South Africa, 17-28 January 1994, H.B. Geyer ed., Springer 1995.
35. B. Halprin, Statistics of quasiparticles and the hierarchy of fractional quantum Hall states, Phys. Rev. Lett. 52 (1984) 1583.
36. N. Read, Excitation structure of the hierarchy scheme for the fractional quantum Hall effect, Phys. Rev. Lett. 65 (1990) 1502.
37. N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys. 09 (1999) 032 [hep-th/9908142].
38. M.A. Olshanetsky and A.M. Perelomov, Classical integrable finite dimensional systems related to lie algebras, Phys. Re.pt. 71 (1981) 313;
39. Quantum integrable systems related to Lie algebras, Phys. Rept. 94 (1983) 313;
40. F. Calogero, Solution of the one-dimensional N body problems with quadratic and/or inversely quadratic pair potentials, J. Math. Phys. 12 (1971) 419;
41. A.P. Polychronakos, Integrable systems from gauged matrix models, Phys. Lett. B 266 (1991) 29.
42. J. Polchinski, String theory, Cambridge University Press, Cambridge 1998.
43. A.P. Polychronakos, Quantum Hall states as matrix Chern-Simons theory, J. High Energy Phys. 04 (2001) 011 [hep-th/0103013].
44. A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230].