A concise review of an M5-brane in a large C-field background

Chinese Journal of Physics

Volumn 48, Issue 1, 2010, Pages 1-16

  Ho, Pei Ming ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953663493     PISSN: 05779073     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (58)

1. P. S. Howe and E. Sezgin, "D = 11, p = 5," Phys. Lett. B 394, 62 (1997) [arXiv:hep-th/9611008]
2. P. Pasti, D. P. Sorokin and M. Tonin, "Covariant action for a D = 11 ve-brane with the chiral eld," Phys. Lett. B 398, 41 (1997) [arXiv:hep-th/9701037].
3. I. A. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. P. Sorokin and M. Tonin, "Covariant action for the super-ve-brane of M-theory," Phys. Rev. Lett. 78, 4332 (1997) [arXiv:hep-th/9701149].
4. M. Aganagic, J. Park, C. Popescu and J. H. Schwarz, "World-volume action of the M-theory ve-brane," Nucl. Phys. B 496, 191 (1997) [arXiv:hep-th/9701166]
5. P. S. Howe, E. Sezgin and P. C.West, "Covariant eld equations of the M-theory ve-brane," Phys. Lett. B 399, 49 (1997) [arXiv:hep-th/9702008]
6. I. A. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. P. Sorokin and M. Tonin, "On the equivalence of different formulations of the M theory ve-brane," Phys. Lett. B 408, 135 (1997) [arXiv:hep-th/9703127].
7. P. M. Ho and Y. Matsuo, "M5 from M2," arXiv:0804.3629 [hep-th].
8. P. M. Ho, Y. Imamura, Y. Matsuo and S. Shiba, "M5-brane in three-form ux and multiple M2-branes," JHEP 0808, 014 (2008) [arXiv:0805.2898 [hep-th]].
9. J. Bagger and N. Lambert, "Modeling multiple M2's," Phys. Rev. D 75, 045020 (2007) [arXiv:hep-th/0611108]
10. J. Bagger and N. Lambert, "Gauge Symmetry and Supersymmetry of Multiple M2-Branes," Phys. Rev. D 77, 065008 (2008) [arXiv:0711.0955 [hep-th]]
11. J. Bagger and N. Lambert, "Comments On Multiple M2-branes,"JHEP 0802, 105 (2008) [arXiv:0712.3738 [hep-th]].
12. A. Gustavsson, "Algebraic structures on parallelM2-branes," arXiv:0709.1260 [hep-th]
13. A. Gus-tavsson, "Selfdual strings and loop space Nahm equations," arXiv:0802.3456 [hep-th].
14. P. M. Ho, "Nambu Bracket for M Theory," arXiv:0912.0055 [hep-th].
15. C. S. Chu, P. M. Ho, Y. Matsuo and S. Shiba, "Truncated Nambu-Poisson Bracket and Entropy Formula for Multiple Membranes," JHEP 0808, 076 (2008) [arXiv:0807.0812 [hep-th]].
16. C. S. Chu and P. M. Ho, "Noncommutative open string and D-brane," Nucl. Phys. B 550, 151 (1999) [arXiv:hep-th/9812219]
17. C. S. Chu and P. M. Ho, "Constrained quantization of open string in background B eld and noncommutative D-brane," Nucl. Phys. B 568, 447 (2000) [arXiv:hep-th/9906192].
18. V. Schomerus, "D-branes and deformation quantization," JHEP 9906, 030 (1999) [arXiv:hep-th/9903205].
19. N. Seiberg and E. Witten, "String theory and noncommutative geometry," JHEP 9909, 032 (1999) [arXiv:hep-th/9908142].
20. L. Cornalba and R. Schiappa, "Nonassociative star product deformations for D-brane worldvol-umes in curved backgrounds," Commun. Math. Phys. 225, 33 (2002) [arXiv:hep-th/0101219].
21. P. M. Ho, "Making non-associative algebra associative," JHEP 0111, 026 (2001) [arXiv:hep-th/0103024].
22. E. Bergshoeff, D. S. Berman, J. P. van der Schaar and P. Sundell, "A noncommutative M-theory ve-brane," Nucl. Phys. B 590, 173 (2000) [arXiv:hep-th/0005026];
23. S. Kawamoto and N. Sasakura, "Open membranes in a constant C-eld background and non-commutative boundary strings," JHEP 0007, 014 (2000) [arXiv:hep-th/0005123]
24. N. Ikeda, "Deformation of BF theories, topological open membrane and a generalization of the star deformation," JHEP 0107, 037 (2001) [arXiv:hep-th/0105286]
25. B. Pioline, "Comments on the topological open membrane," Phys. Rev. D 66, 025010 (2002) [arXiv:hep-th/0201257];
26. D. S. Berman and B. Pioline, "Open membranes, ribbons and deformed Schild strings," Phys. Rev. D 70, 045007 (2004) [arXiv:hep-th/0404049].
27. Y. Matsuo and Y. Shibusa, "Volume preserving diffeomorphism and noncommutative branes," JHEP 0102, 006 (2001) [arXiv:hep-th/0010040]
28. M. Sakakibara, "Remarks on a deformation quantization of the canonical Nambu bracket," Prog. Theor. Phys. 104 (2000) 1067.
29. D. S. Berman, "M-theory branes and their interactions," Phys. Rept. 456, 89 (2008) [arXiv:0710.1707 [hep-th]].
30. Z. Yin, "A note on space noncommutativity," Phys. Lett. B 466, 234 (1999) [arXiv:hep-th/9908152]
31. D. Bigatti and L. Susskind, "Magnetic elds, branes and noncommutative ge-ometry," Phys. Rev. D 62, 066004 (2000) [arXiv:hep-th/9908056].
32. P. M. Ho and Y. Matsuo, "A toy model of open membrane eld theory in constant 3-form ux," Gen. Rel. Grav. 39, 913 (2007) [arXiv:hep-th/0701130].
33. Y. Nambu, "Generalized Hamiltonian dynamics," Phys. Rev. D 7, 2405 (1973).
34. L. Takhtajan, "On Foundation Of The Generalized Nambu Mechanics (Second Version)," Com-mun. Math. Phys. 160, 295 (1994) [arXiv:hep-th/9301111].
35. V. T. Filippov, "n-Lie algebras," Sib. Mat. Zh.,26, No. 6, 126140 (1985).
36. P. M. Ho, R. C. Hou and Y. Matsuo, "Lie 3-Algebra and Multiple M2-branes," JHEP 0806, 020 (2008) [arXiv:0804.2110 [hep-th]].
37. R. Weitzenbök, "Invariantentheorie," P. Noordhoff, Gröningen, 1923. Ph. Gautheron, "Some remarks concerning Nambu mechanics," Lett. in Math. Phys. 37 (1996), 103
38. D. Alekseevsky, P. Guha, "On Decomposability of Nambu-Poisson Tensor," Acta. Math. Univ. Commenianae 65 (1996), 1
39. R. Ibánez, M. de León, J. C. Marrero, D. M. de Diego, "Dynamics of generalized Poisson and Nambu-Poisson brackets," J. of Math. Physics 38 (1997), 2332
40. N. Nakanishi, "On Nambu-Poisson Manifolds," Reviews in Mathematical Physics 10 (1998), 499
41. G. Marmo, G. Vilasi, A. M. Vinogradov, "The local structure of n-Poisson and n-Jacobi manifolds," J. Geom. Physics 25 (1998), 141.
42. For a review of the Nambu-Poisson bracket, see: I. Vaisman, "A survey on Nambu-Poisson brackets," Acta. Math. Univ. Comenianae 2 (1999), 213.
43. A. M. Low, arXiv:0909.1941 [hep-th].
44. D. Zwanziger, "Local Lagrangian quantum eld theory of electric and magnetic charges," Phys. Rev. D 3, 880 (1971).
45. S. Deser and C. Teitelboim, "Duality Transformations Of Abelian And Nonabelian Gauge Fields," Phys. Rev. D 13, 1592 (1976)
46. R. Floreanini and R. Jackiw, "Self-dual Fields As Charge Density Solitons," Phys. Rev. Lett. 59, 1873 (1987)
47. M. Henneaux and C. Teitelboim, "DYNAMICS OF CHIRAL (SELFDUAL) P FORMS," Phys. Lett. B 206, 650 (1988)
48. A. A. Tseytlin, "Duality Symmetric Formulation Of String World Sheet Dynamics," Phys. Lett. B 242, 163 (1990).
49. A. A. Tseytlin, "Duality Symmetric Closed String Theory And Interacting Chiral Scalars," Nucl. Phys. B 350, 395 (1991)
50. J. H. Schwarz and A. Sen, "Duality symmetric actions," Nucl. Phys. B 411, 35 (1994) [arXiv:hep-th/9304154].
51. P. Pasti, I. Samsonov, D. Sorokin and M. Tonin, "BLG-motivated Lagrangian formulation for the chiral two-form gauge eld in D=6 and M5-branes," Phys. Rev. D 80, 086008 (2009) [arXiv:0907.4596 [hep-th]].
52. P. S. Howe, N. D. Lambert and P. C. West, "The self-dual string soliton," Nucl. Phys. B 515, 203 (1998) [arXiv:hep-th/9709014].
53. Y. Michishita, "The M2-brane soliton on the M5-brane with constant 3-form," JHEP 0009, 036 (2000) [arXiv:hep-th/0008247]
54. D. Youm, "BPS solitons in M5-brane worldvolume theory with constant three-form eld," Phys. Rev. D 63, 045004 (2001) [arXiv:hep-th/0009082].
55. K. Furuuchi and T. Takimi, "String solitons in the M5-brane worldvolume action with Nambu-Poisson structure and Seiberg-Witten map," JHEP 0908, 050 (2009) [arXiv:0906.3172 [hep-th]].
56. C. S. Chu and D. J. Smith, "Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes," JHEP 0904, 097 (2009) [arXiv:0901.1847 [hep-th]].
57. I. A. Bandos and P. K. Townsend, "Light-cone M5 and multiple M2-branes," Class. Quant. Grav. 25, 245003 (2008) [arXiv:0806.4777 [hep-th]].
58. I. A. Bandos and P. K. Townsend, "SDiff Gauge Theory and the M2 Condensate," JHEP 0902, 013 (2009) [arXiv:0808.1583 [hep-th]]