Towards the quantum geometry of the M5-brane in a constant C-field from multiple membranes

Journal of High Energy Physics

Volumn 2009, Issue 4, 2009, Pages

  Chu, Chong Sun ^a   Smith, Douglas J ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Brane dynamics in gfauge theories; D branes; M theory; Non commutative geometry

Indexed keywords

EID: 67649618061     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2009/04/097     Document Type: Article

References (90)

1. J. Bagger and N. Lambert, 2007 Modeling multiple M2's, Phys. Rev. D 75 045020 [hep-th/0611108]
2. J. Bagger and N. Lambert, 2008 Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 065008 [0711.0955]
3. J. Bagger and N. Lambert, 2008 Comments on multiple M2-branes, J. High Energy Phys. JHEP02(2008)105 [0712.3738]
4. A. Gustavsson, 2009 Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 66 [0709.1260]
5. A. Basu and J.A. Harvey, 2005 The M2-M5 brane system and a generalized Nahm's equation, Nucl. Phys. B 713 136 [hep-th/0412310]
6. N. Lambert and D. Tong, 2008 Membranes on an orbifold, Phys. Rev. Lett. 101 041602 [0804.1114]
7. J. Distler, S. Mukhi, C. Papageorgakis and M. Van Raamsdonk, 2008 M2-branes on M-folds, J. High Energy Phys. JHEP05(2008)038 [0804.1256]
8. J. Gomis, G. Milanesi and J.G. Russo, 2008 Bagger-Lambert theory for general lie algebras, J. High Energy Phys. JHEP06(2008)075 [0805.1012]
9. S. Benvenuti, D. Rodriguez-Gomez, E. Tonni and H. Verlinde, 2009 =8 superconformal gauge theories and M2 branes, J. High Energy Phys. JHEP01(2009)078 [0805.1087]
10. P.-M. Ho, Y. Imamura and Y. Matsuo, 2008 M2 to D2 revisited, J. High Energy Phys. JHEP07(2008)003 [0805.1202]
11. M.A. Bandres, A.E. Lipstein and J.H. Schwarz, 2008 Ghost-free superconformal action for multiple M2-branes, J. High Energy Phys. JHEP07(2008)117 [0806.0054]
12. J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonk and H. Verlinde, 2008 Supersymmetric Yang-Mills Theory From Lorentzian Three- Algebras, J. High Energy Phys. JHEP08(2008)094 [0806.0738]
13. B. Ezhuthachan, S. Mukhi and C. Papageorgakis, 2008 D2 to D2, J. High Energy Phys. JHEP07(2008)041 [0806.1639]
14. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, 2008 =6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, J. High Energy Phys. JHEP10(2008)091 [0806.1218]
15. J. Bagger and N. Lambert, 2009 Three-algebras and =6 Chern-Simons gauge theories, Phys. Rev. D 79 025002 [0807.0163]
16. P.S. Howe and E. Sezgin, 1997 D=11, p=5, Phys. Lett. B 394 62 [hep-th/9611008]
17. P.S. Howe, E. Sezgin and P.C. West, 1997 Covariant field equations of the M-theory five-brane, Phys. Lett. B 399 49 [hep-th/9702008]
18. M. Aganagic, J. Park, C. Popescu and J.H. Schwarz, 1997 World-volume action of the M-theory five-brane, Nucl. Phys. B 496 191 [hep-th/9701166]
19. P. Pasti, D.P. Sorokin and M. Tonin, 1997 Covariant action for a D=11 five-brane with the chiral field, Phys. Lett. B 398 41 [hep-th/9701037]
20. I.A. Bandos et al., 1997 Covariant action for the super-five-brane of M-theory, Phys. Rev. Lett. 78 4332 [hep-th/9701149]
21. C.S. Chu and E. Sezgin, 1997 M-fivebrane from the open supermembrane, J. High Energy Phys. JHEP12(1997)001 [hep-th/9710223]
22. A. Connes, M.R. Douglas and A.S. Schwarz, 1998 Noncommutative geometry and matrix theory: compactification on tori, J. High Energy Phys. JHEP02(1998)003 [hep-th/9711162]
23. M.R. Douglas and C.M. Hull, 1998 D-branes and the noncommutative torus, J. High Energy Phys. JHEP02(1998)008 [hep-th/9711165]
24. N. Seiberg and E. Witten, 1999 String theory and noncommutative geometry, J. High Energy Phys. JHEP09(1999)032 [hep-th/9908142]
25. C.-S. Chu and P.-M. Ho, 1999 Noncommutative open string and D-brane, Nucl. Phys. B 550 151 [hep-th/9812219]
26. C.-S. Chu and P.-M. Ho, 2000 Constrained quantization of open string in background B field and noncommutative D-brane, Nucl. Phys. B 568 447 [hep-th/9906192]
27. C.-S. Chu, Noncommutative open string: neutral and charged, [hep-th/0001144]
28. E. Bergshoeff, D.S. Berman, J.P. van der Schaar and P. Sundell, 2000 A noncommutative M-theory five-brane, Nucl. Phys. B 590 173 [hep-th/0005026]
29. S. Kawamoto and N. Sasakura, 2000 Open membranes in a constant C-field background and noncommutative boundary strings, J. High Energy Phys. JHEP07(2000)014 [hep-th/0005123]
30. C.G. Callan and J.M. Maldacena, 1998 Brane dynamics from the Born-Infeld action, Nucl. Phys. B 513 198 [hep-th/9708147]
31. N.R. Constable, R.C. Myers and O. Tafjord, 2000 The noncommutative bion core, Phys. Rev. D 61 106009 [hep-th/9911136]
32. N.R. Constable, R.C. Myers and O. Tafjord, Fuzzy funnels: non-abelian brane intersections, [hep-th/0105035]
33. S. Moriyama, 2000 Noncommutative monopole from nonlinear monopole, Phys. Lett. B 485 278 [hep-th/0003231]
34. R.C. Myers, 1999 Dielectric-branes, J. High Energy Phys. JHEP12(1999)022 [hep-th/9910053]
35. J.L. Karczmarek and C.G. Callan Jr., 2002 Tilting the noncommutative bion, J. High Energy Phys. JHEP05(2002)038 [hep-th/0111133]
36. P.S. Howe, N.D. Lambert and P.C. West, 1998 The self-dual string soliton, Nucl. Phys. B 515 203 [hep-th/9709014]
37. Y. Michishita, 2000 The M2-brane soliton on the M5-brane with constant 3-form, J. High Energy Phys. JHEP09(2000)036 [hep-th/0008247]
38. D. Youm, 2001 BPS solitons in M5-brane worldvolume theory with constant three-form field, Phys. Rev. D 63 045004 [hep-th/0009082]
39. D.-E. Diaconescu, 1997 D-branes, monopoles and Nahm equations, Nucl. Phys. B 503 220 [hep-th/9608163]
40. A. Kapustin and S. Sethi, 1998 The Higgs branch of impurity theories, Adv. Theor. Math. Phys. 2 571 [hep-th/9804027]
41. D. Tsimpis, 1998 Nahm equations and boundary conditions, Phys. Lett. B 433 287 [hep-th/9804081]
42. M.R. Garousi, 2009 On non-linear action of multiple M2-branes, Nucl. Phys. B 809 519 [0809.0985]
43. R. Iengo and J.G. Russo, 2008 Non-linear theory for multiple M2 branes, J. High Energy Phys. JHEP10(2008)030 [0808.2473]
44. F. Lizzi, N.E. Mavromatos and R.J. Szabo, 1998 Matrix σ-models for multi D-brane dynamics, Mod. Phys. Lett. A 13 829 [hep-th/9711012]
45. T. Banks, W. Fischler, S.H. Shenker and L. Susskind, 1997 M theory as a matrix model: a conjecture, Phys. Rev. D 55 5112 [hep-th/9610043]
46. L. Motl, Proposals on nonperturbative superstring interactions, [hep-th/9701025]
47. T. Banks, N. Seiberg and S.H. Shenker, 1997 Branes from matrices, Nucl. Phys. B 490 91 [hep-th/9612157]
48. R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, 1997 Matrix string theory, Nucl. Phys. B 500 43 [hep-th/9703030]
49. Z. Guralnik and S. Ramgoolam, 2001 On the polarization of unstable D 0-branes into non- commutative odd spheres, J. High Energy Phys. JHEP02(2001)032 [hep-th/0101001]
50. D.S. Berman and N.B. Copland, 2006 A note on the M2-M5 brane system and fuzzy spheres, Phys. Lett. B 639 553 [hep-th/0605086]
51. C. Krishnan and C. Maccaferri, 2008 Membranes on Calibrations, J. High Energy Phys. JHEP07(2008)005 [0805.3125]
52. J.P. Gauntlett and J.B. Gutowski, Constraining maximally supersymmetric membrane actions, [0804.3078]
53. G. Papadopoulos, 2008 M2-branes, 3-lie algebras and plucker relations, J. High Energy Phys. JHEP05(2008)054 [0804.2662]
54. C.-S. Chu, P.-M. Ho, Y. Matsuo and S. Shiba, 2008 Truncated Nambu-Poisson bracket and entropy formula for multiple membranes, J. High Energy Phys. JHEP08(2008)076 [0807.0812]
55. M. Li and T. Wang, 2008 M2-branes coupled to antisymmetric fluxes, J. High Energy Phys. JHEP07(2008)093 [0805.3427]
56. P.-M. Ho and Y. Matsuo, 2008 M5 from M2, J. High Energy Phys. JHEP06(2008)105 [0804.3629]
57. P.-M. Ho, Y. Imamura, Y. Matsuo and S. Shiba, 2008 M5-brane in three-form flux and multiple M2-branes, J. High Energy Phys. JHEP08(2008)014 [0805.2898]
58. J.M. Figueroa-O'Farrill, Three lectures on 3-algebras, [0812.2865]
59. P. de Medeiros, J. Figueroa-O'Farrill, E. Mendez-Escobar and P. Ritter, Metric 3-Lie algebras for unitary Bagger-Lambert theories, [0902.4674]
60. P. de Medeiros, J. Figueroa-O'Farrill, E. Mendez-Escobar and P. Ritter, On the Lie-algebraic origin of metric 3-algebras, [0809.1086]
61. P. de Medeiros, J.M. Figueroa-O'Farrill and E. Mendez-Escobar, 2008 Metric lie 3-algebras in Bagger-Lambert theory, J. High Energy Phys. JHEP08(2008)045 [0806.3242]
62. P. de Medeiros, J.M. Figueroa-O'Farrill and E. Mendez-Escobar, 2008 Lorentzian Lie 3-algebras and their Bagger-Lambert moduli space, J. High Energy Phys. JHEP07(2008)111 [0805.4363]
63. Y. Nambu, 1973 Generalized Hamiltonian dynamics, Phys. Rev. D 7 2405
64. L. Takhtajan, 1994 On foundation of the generalized Nambu mechanics (second version), Commun. Math. Phys. 160 295 [hep-th/9301111] (Pubitemid 24766454)
65. J. Hoppe, 1997 On M-algebras, the quantisation of Nambu-Mechanics and volume preserving diffeomorphisms, Helv. Phys. Acta 70 302 [hep-th/9602020]
66. D. Minic, M-theory and deformation quantization, [hep-th/9909022]
67. L.M. Baker and D.B. Fairlie, 2001 Hamilton-Jacobi equations and brane associated Lagrangians, Nucl. Phys. B 596 348 [hep-th/0003048]
68. Y. Matsuo and Y. Shibusa, 2001 Volume preserving diffeomorphism and noncommutative branes, J. High Energy Phys. JHEP02(2001)006 [hep-th/0010040]
69. B. Pioline, 2002 Comments on the topological open membrane, Phys. Rev. D 66 025010 [hep-th/0201257]
70. T.L. Curtright and C.K. Zachos, 2002 Deformation quantization of superintegrable systems and Nambu mechanics, New J. Phys. 4 83 [hep-th/0205063]
71. T. Curtright and C.K. Zachos, 2003 Classical and quantum Nambu mechanics, Phys. Rev. D 68 085001 [hep-th/0212267]
72. G. Dito, M. Flato, D. Sternheimer and L. Takhtajan, 1997 Deformation quantization and Nambu mechanics, Commun. Math. Phys. 183 1 [hep-th/9602016]
73. H. Awata, M. Li, D. Minic and T. Yoneya, 2001 On the quantization of Nambu brackets, J. High Energy Phys. JHEP02(2001)013 [hep-th/9906248]
74. Y. Kawamura, 2003 Structure of generalized matrix mechanics, Prog. Theor. Phys. 109 1 [hep-th/0206184]
75. Y. Kawamura, 2003 Cubic matrix, Nambu mechanics and beyond, Prog. Theor. Phys. 109 153 [hep-th/0207054]
76. F. Bayen and M. Flato, 1975 Remarks concerning Nambu's generalized mechanics, Phys. Rev. D 11 3049
77. N. Mukunda and G. Sudarshan, 1976 Relation between Nambu and Hamiltonian mechanics, Phys. Rev. D 13 2846
78. S. Minwalla, M. Van Raamsdonk and N. Seiberg, 2000 Noncommutative perturbative dynamics, J. High Energy Phys. JHEP02(2000)020 [hep-th/9912072]
79. K. Hashimoto and T. Hirayama, 2000 Branes and BPS configurations of noncommutative/commutative gauge theories, Nucl. Phys. B 587 207 [hep-th/0002090]
80. S. Moriyama, 2000 Noncommutative monopole from nonlinear monopole, Phys. Lett. B 485 278 [hep-th/0003231]
81. P.-M. Ho and Y. Matsuo, 2007 A toy model of open membrane field theory in constant 3- form flux, Gen. Rel. Grav. 39 913 [hep-th/0701130]
82. H. Ooguri and C. Vafa, 2003 The C-deformation of gluino and non-planar diagrams, Adv. Theor. Math. Phys. 7 53 [hep-th/0302109]
83. H. Ooguri and C. Vafa, 2004 Gravity induced C-deformation, Adv. Theor. Math. Phys. 7 405 [hep-th/0303063]
84. J. de Boer, P.A. Grassi and P. van Nieuwenhuizen, 2003 Non-commutative superspace from string theory, Phys. Lett. B 574 98 [hep-th/0302078]
85. N. Seiberg, 2003 Noncommutative superspace, N=1/2 supersymmetry, field theory and string theory, J. High Energy Phys. JHEP06(2003)010 [hep-th/0305248]
86. N. Berkovits and N. Seiberg, 2003 Superstrings in graviphoton background and N=1/2 + 3/2 supersymmetry, J. High Energy Phys. JHEP07(2003)010 [hep-th/0306226]
87. S. Ferrara, E. Ivanov, O. Lechtenfeld, E. Sokatchev and B. Zupnik, 2005 Non-anticommutative chiral singlet deformation of N = (1,1) gauge theory, Nucl. Phys. B 704 154 [hep-th/0405049]
88. K. Ito and S. Sasaki, 2006 Non(anti)commutative N=2 supersymmetric gauge theory from superstrings in the graviphoton background, J. High Energy Phys. JHEP11(2006)004 [hep-th/0608143]
89. K. Ito, Y. Kobayashi and S. Sasaki, 2007 Deformation of N=4 super Yang-Mills theory in graviphoton background, J. High Energy Phys. JHEP04(2007)011 [hep-th/0612267]
90. C.-S. Chu, S.-H. Dai and D.J. Smith, 2008 AdS/CFT Duality for non-anticommutative supersymmetric gauge theory, J. High Energy Phys. JHEP05(2008)029 [0803.0895]