Boundary conditions for interacting membranes

  • David S. Berman
  • Malcolm J. Perry
  • Ergin Sezgin
  • Daniel C. Thompson
Article

Abstract

We investigate supersymmetric boundary conditions in both the Bagger-Lambert and the ABJM theories of interacting membranes. We find boundary conditions associated to the fivebrane, the ninebrane and the M-theory wave. For the ABJM theory we are able to understand the enhancement of supersymmetry to produce the (4,4) supersymmetry of the self-dual string. We also include supersymmetric boundary conditions on the gauge fields that cancel the classical gauge anomaly of the Chern-Simons terms.

Keywords

M-Theory Brane Dynamics in Gauge Theories 

References

  1. [1]
    D.S. Berman, M-theory branes and their interactions, Phys. Rept. 456 (2008) 89 [arXiv:0710.1707] [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    P.K. Townsend, D-branes from M-branes, Phys. Lett. B 373 (1996) 68 [hep-th/9512062] [SPIRES].MathSciNetADSGoogle Scholar
  3. [3]
    A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059] [SPIRES].MathSciNetADSGoogle Scholar
  4. [4]
    C.S. Chu and E. Sezgin, M-fivebrane from the open supermembrane, JHEP 12 (1997) 001 [hep-th/9710223] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    C.S. Chu, P.S. Howe, E. Sezgin and P.C. West, Open superbranes, Phys. Lett. B 429 (1998) 273 [hep-th/9803041] [SPIRES].MathSciNetADSGoogle Scholar
  6. [6]
    P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [SPIRES].ADSGoogle Scholar
  7. [7]
    P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [SPIRES].ADSGoogle Scholar
  8. [8]
    M. Cederwall, Boundaries of 11-dimensional membranes, Mod. Phys. Lett. A 12 (1997) 2641 [hep-th/9704161] [SPIRES].MathSciNetADSGoogle Scholar
  9. [9]
    J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [SPIRES].MathSciNetADSGoogle Scholar
  10. [10]
    J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES].MathSciNetADSGoogle Scholar
  11. [11]
    J. Bagger and N. Lambert, Comments on multiple M2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  13. [13]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  14. [14]
    D.S. Berman, L.C. Tadrowski and D.C. Thompson, Aspects of multiple membranes, Nucl. Phys. B 802 (2008) 106 [arXiv:0803.3611] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  15. [15]
    D.S. Berman and D.C. Thompson, Membranes with a boundary, Nucl. Phys. B 820 (2009) 503 [arXiv:0904.0241] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    H. Nastase, C. Papageorgakis and S. Ramgoolam, The fuzzy S2 structure of M2-M5 systems in ABJM membrane theories, JHEP 05 (2009) 123 [arXiv:0903.3966] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    P.-M. Ho, Y. Imamura, Y. Matsuo and S. Shiba, M5-brane in three-form flux and multiple M2-branes, JHEP 08 (2008) 014 [arXiv:0805.2898] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    P.-M. Ho and Y. Matsuo, M5 from M2, JHEP 06 (2008) 105 [arXiv:0804.3629] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  19. [19]
    C.-S. Chu and D.J. Smith, Multiple self-dual strings on M5-branes, JHEP 01 (2010) 001 [arXiv:0909.2333] [SPIRES].CrossRefGoogle Scholar
  20. [20]
    S. Terashima, On M5-branes in N = 6 membrane action, JHEP 08 (2008) 080 [arXiv:0807.0197] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  21. [21]
    S. Terashima and F. Yagi, M5-brane solution in ABJM theory and three-algebra, JHEP 12 (2009) 059 [arXiv:0909.3101] [SPIRES].CrossRefADSGoogle Scholar
  22. [22]
    K. Hanaki and H. Lin, M2-M5 systems in N = 6 Chern-Simons theory, JHEP 09 (2008) 067 [arXiv:0807.2074] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  23. [23]
    D. Gaiotto and E. Witten, Supersymmetric boundary conditions in N = 4 super Yang-Mills theory, arXiv:0804.2902 [SPIRES].
  24. [24]
    W. Nahm, A simple formalism for the BPS monopole, Phys. Lett. B 90 (1980) 413 [SPIRES].ADSGoogle Scholar
  25. [25]
    A. Basu and J.A. Harvey, The M2-M5 brane system and a generalized Nahm’s equation, Nucl. Phys. B 713 (2005) 136 [hep-th/0412310] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  26. [26]
    D.-E. Diaconescu, D-branes, monopoles and Nahm equations, Nucl. Phys. B 503 (1997) 220 [hep-th/9608163] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  27. [27]
    P.S. Howe, N.D. Lambert and P.C. West, The self-dual string soliton, Nucl. Phys. B 515 (1998) 203 [hep-th/9709014] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  28. [28]
    J.P. Gauntlett, Intersecting branes, hep-th/9705011 [SPIRES].
  29. [29]
    G.W. Gibbons and G. Papadopoulos, Calibrations and intersecting branes, Commun. Math. Phys. 202 (1999) 593 [hep-th/9803163] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  30. [30]
    P.-A. Nagy, Prolongations of Lie algebras and applications, http://arxiv:org.abs/0712.1398.
  31. [31]
    G. Papadopoulos, M2-branes, 3-Lie algebras and Plucker relations, JHEP 05 (2008) 054 [arXiv:0804.2662] [SPIRES].CrossRefADSGoogle Scholar
  32. [32]
    J.P. Gauntlett and J.B. Gutowski, Constraining maximally supersymmetric membrane actions, JHEP 06 (2008) 053 [arXiv:0804.3078] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  33. [33]
    S. Benvenuti, D. Rodriguez-Gomez, E. Tonni and H. Verlinde, N=8 superconformal gauge theories and M2 branes, JHEP 01 (2009) 078 [arXiv:0805.1087] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  34. [34]
    J. Gomis, G. Milanesi and J.G. Russo, Bagger-Lambert theory for general Lie algebras, JHEP 06 (2008) 075 [arXiv:0805.1012] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  35. [35]
    M.A. Bandres, A.E. Lipstein and J.H. Schwarz, Ghost-free superconformal action for multiple M2-branes, JHEP 07 (2008) 117 [arXiv:0806.0054] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  36. [36]
    M. Van Raamsdonk, Comments on the Bagger-Lambert theory and multiple M2-branes, JHEP 05 (2008) 105 [arXiv:0803.3803] [SPIRES].CrossRefADSGoogle Scholar
  37. [37]
    D.S. Berman and J.A. Harvey, The self-dual string and anomalies in the M5-brane, JHEP 11 (2004) 015 [hep-th/0408198] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  38. [38]
    E. Bergshoeff, E. Sezgin and P.K. Townsend, Supermembranes and eleven-dimensional supergravity, Phys. Lett. B 189 (1987) 75 [SPIRES].MathSciNetADSGoogle Scholar
  39. [39]
    F. Passerini, M2-Brane superalgebra from Bagger-Lambert theory, JHEP 08 (2008) 062 [arXiv:0806.0363] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  40. [40]
    J. Distler, S. Mukhi, C. Papageorgakis and M. Van Raamsdonk, M2-branes on M-folds, JHEP 05 (2008) 038 [arXiv:0804.1256] [SPIRES].CrossRefADSGoogle Scholar
  41. [41]
    N. Lambert and D. Tong, Membranes on an orbifold, Phys. Rev. Lett. 101 (2008) 041602 [arXiv:0804.1114] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  42. [42]
    O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  43. [43]
    K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N=5,6 superconformal Chern-Simons theories and M2-branes on orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  44. [44]
    J. Bagger and N. Lambert, Three-algebras and N = 6 Chern-Simons gauge theories, Phys. Rev. D 79 (2009) 025002 [arXiv:0807.0163] [SPIRES].MathSciNetADSGoogle Scholar
  45. [45]
    M. Benna, I. Klebanov, T. Klose and M. Smedback, Superconformal Chern-Simons theories and AdS 4/CFT 3 correspondence, JHEP 09 (2008) 072 [arXiv:0806.1519] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  46. [46]
    M.A. Bandres, A.E. Lipstein and J.H. Schwarz, Studies of the ABJM theory in a formulation with manifest SU(4) R-symmetry, JHEP 09 (2008) 027 [arXiv:0807.0880] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  47. [47]
    A.M. Low, N=6 membrane worldvolume superalgebra, JHEP 04 (2009) 105 [arXiv:0903.0988] [SPIRES].CrossRefADSGoogle Scholar
  48. [48]
    I.R. Klebanov and G. Torri, M2-branes and AdS/CFT, Int. J. Mod. Phys. A 25 (2010) 332 [arXiv:0909.1580] [SPIRES].ADSGoogle Scholar
  49. [49]
    A. Gustavsson and S.-J. Rey, Enhanced N = 8 supersymmetry of ABJM theory on R 8 and R 8/Z 2, arXiv:0906.3568 [SPIRES].
  50. [50]
    O.-K. Kwon, P. Oh and J. Sohn, Notes on supersymmetry enhancement of ABJM theory, JHEP 08 (2009) 093 [arXiv:0906.4333] [SPIRES].CrossRefADSGoogle Scholar
  51. [51]
    O. Ganor and L. Motl, Equations of the (2,0) theory and knitted fivebranes, JHEP 05 (1998) 009 [hep-th/9803108] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  52. [52]
    K.A. Intriligator, Anomaly matching and a Hopf-Wess-Zumino term in 6d, N = (2,0) field theories, Nucl. Phys. B 581 (2000) 257 [hep-th/0001205] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  53. [53]
    D.S. Berman and J.A. Harvey, The self-dual string and anomalies in the M5-brane, JHEP 11 (2004) 015 [hep-th/0408198] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  54. [54]
    E. Bergshoeff, D.S. Berman, J.P. van der Schaar and P. Sundell, A noncommutative M-theory five-brane, Nucl. Phys. B 590 (2000) 173 [hep-th/0005026] [SPIRES].CrossRefADSGoogle Scholar
  55. [55]
    Y. Michishita, The M2-brane soliton on the M5-brane with constant 3-form, JHEP 09 (2000) 036 [hep-th/0008247] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  56. [56]
    D. Youm, BPS solitons in M5-brane worldvolume theory with constant three-form field, Phys. Rev. D 63 (2001) 045004 [hep-th/0009082] [SPIRES].MathSciNetADSGoogle Scholar
  57. [57]
    N. Lambert and P. Richmond, M2-Branes and background fields, JHEP 10 (2009) 084 [arXiv:0908.2896] [SPIRES].CrossRefADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • David S. Berman
    • 1
  • Malcolm J. Perry
    • 2
  • Ergin Sezgin
    • 3
  • Daniel C. Thompson
    • 1
  1. 1.Queen Mary University of London, Department of PhysicsLondonU.K.
  2. 2.DAMTP, Centre for Mathematical ScienceUniversity of CambridgeEnglandU.K.
  3. 3.George P. and Cynthia W. Mitchell Institute for Fundamental Physics and AstronomyTexas A&M UniversityCollege StationU.S.A.

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