Skip to main content
SpringerLink
Log in

Non-abelian action for multiple five-branes with self-dual tensors

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We construct an action for non-abelian 2-form in 6-dimensions. Our action consists of a non-abelian generalization of the abelian action of Perry and Schwarz for a single five-brane. It admits a self-duality equation on the field strength as the equation of motion. It has a modified 6d Lorentz symmetry. On dimensional reduction on a circle, our action gives the standard 5d Yang-Mills action plus higher order corrections. Based on these properties, we propose that our theory describes the gauge sector of multiple M5-branes in flat space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G.W. Gibbons and P.K. Townsend, Vacuum interpolation in supergravity via super p-branes, Phys. Rev. Lett. 71 (1993) 3754 [hep-th/9307049].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. D.M. Kaplan and J. Michelson, Zero modes for the D = 11 membrane and five-brane, Phys. Rev. D 53 (1996) 3474 [hep-th/9510053].

    MathSciNet  ADS  Google Scholar 

  4. E. Witten, Five-brane effective action in M-theory, J. Geom. Phys. 22 (1997) 103 [hep-th/9610234] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. P.S. Howe and E. Sezgin, D = 11, p = 5, Phys. Lett. B 394 (1997) 62 [hep-th/9611008] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  6. P.S. Howe, E. Sezgin and P.C. West, Covariant field equations of the M-theory five-brane, Phys. Lett. B 399 (1997) 49 [hep-th/9702008] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. M. Perry and J.H. Schwarz, Interacting chiral gauge fields in six-dimensions and Born-Infeld theory, Nucl. Phys. B 489 (1997) 47 [hep-th/9611065] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. M. Aganagic, J. Park, C. Popescu and J.H. Schwarz, World volume action of the M-theory five-brane, Nucl. Phys. B 496 (1997) 191 [hep-th/9701166] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. P. Pasti, D.P. Sorokin and M. Tonin, On Lorentz invariant actions for chiral p forms, Phys. Rev. D 55 (1997) 6292 [hep-th/9611100] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  10. P. Pasti, D.P. Sorokin and M. Tonin, Covariant action for a D = 11 five-brane with the chiral field, Phys. Lett. B 398 (1997) 41 [hep-th/9701037] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. I.A. Bandos et al., Covariant action for the superfive-brane of M-theory, Phys. Rev. Lett. 78 (1997) 4332 [hep-th/9701149] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. I.A. Bandos et al., On the equivalence of different formulations of the M-theory five-brane, Phys. Lett. B 408 (1997) 135 [hep-th/9703127] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. M. Cederwall, B.E. Nilsson and P. Sundell, An action for the superfive-brane in D = 11 supergravity, JHEP 04 (1998) 007 [hep-th/9712059] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. M. Henneaux and B. Knaepen, All consistent interactions for exterior form gauge fields, Phys. Rev. D 56 (1997) 6076 [hep-th/9706119] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. M. Henneaux, Uniqueness of the Freedman-Townsend interaction vertex for two form gauge fields, Phys. Lett. B 368 (1996) 83 [hep-th/9511145] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  16. X. Bekaert, M. Henneaux and A. Sevrin, Deformations of chiral two forms in six-dimensions, Phys. Lett. B 468 (1999) 228 [hep-th/9909094] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. M. Henneaux and B. Knaepen, A theorem on first order interaction vertices for free p form gauge fields, Int. J. Mod. Phys. A 15 (2000) 3535 [hep-th/9912052] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  18. R.I. Nepomechie, Approaches to a nonabelian antisymmetric tensor gauge field theory, Nucl. Phys. B 212 (1983) 301 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. X. Bekaert, M. Henneaux and A. Sevrin, Chiral forms and their deformations, Commun. Math. Phys. 224 (2001) 683 [hep-th/0004049] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. X. Bekaert and S. Cucu, Deformations of duality symmetric theories, Nucl. Phys. B 610 (2001) 433 [hep-th/0104048] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. C.-H. Chen, P.-M. Ho and T. Takimi, A no-go theorem for M 5-brane theory, JHEP 03 (2010) 104 [arXiv:1001.3244] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  22. C.-S. Chu and D.J. Smith, Multiple self-dual strings on M 5-branes, JHEP 01 (2010) 001 [arXiv:0909.2333] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. C.-S. Chu, A theory of non-abelian tensor gauge field with non-abelian gauge symmetry G × G, arXiv:1108.5131 [INSPIRE].

  25. M. Henneaux and C. Teitelboim, Dynamics of chiral (selfdual) p forms, Phys. Lett. B 206 (1988) 650 [INSPIRE].

    ADS  Google Scholar 

  26. C. Bunster and M. Henneaux, The action for twisted self-duality, Phys. Rev. D 83 (2011) 125015 [arXiv:1103.3621] [INSPIRE].

    ADS  Google Scholar 

  27. M.R. Douglas, On D = 5 super Yang-Mills theory and (2, 0) theory, JHEP 02 (2011) 011 [arXiv:1012.2880] [INSPIRE].

    ADS  Google Scholar 

  28. N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, M 5-branes, D4-branes and quantum 5D super-Yang-Mills, JHEP 01 (2011) 083 [arXiv:1012.2882] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. N. Lambert and C. Papageorgakis, Nonabelian (2, 0) tensor multiplets and 3-algebras, JHEP 08 (2010) 083 [arXiv:1007.2982] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. P.-M. Ho, K.-W. Huang and Y. Matsuo, A non-abelian self-dual gauge theory in 5 + 1 dimensions, JHEP 07 (2011) 021 [arXiv:1104.4040] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. H. Samtleben, E. Sezgin and R. Wimmer, (1, 0) superconformal models in six dimensions, JHEP 12 (2011) 062 [arXiv:1108.4060] [INSPIRE].

    Article  ADS  Google Scholar 

  32. C.-S. Chu and D.J. Smith, Towards the quantum geometry of the M 5-brane in a constant c-field from multiple membranes, JHEP 04 (2009) 097 [arXiv:0901.1847] [INSPIRE].

    Article  ADS  Google Scholar 

  33. J. DeBellis, C. Sämann and R.J. Szabo, Quantized Nambu-Poisson manifolds and n-Lie algebras, J. Math. Phys. 51 (2010) 122303 [arXiv:1001.3275] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. J. DeBellis, C. Sämann and R.J. Szabo, Quantized Nambu-Poisson manifolds in a 3-Lie algebra reduced model, JHEP 04 (2011) 075 [arXiv:1012.2236] [INSPIRE].

    Article  ADS  Google Scholar 

  35. C.-S. Chu and G.S. Sehmbi, D1-strings in large RR 3-form flux, quantum Nambu geometry and M 5-branes in C-field, J. Phys. A 45 (2012) 055401 [arXiv:1110.2687] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  36. P.-M. Ho and Y. Matsuo, M 5 from M 2, JHEP 06 (2008) 105 [arXiv:0804.3629] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. P.-M. Ho, Y. Imamura, Y. Matsuo and S. Shiba, M 5-brane in three-form flux and multiple M 2-branes, JHEP 08 (2008) 014 [arXiv:0805.2898] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. P. Pasti, I. Samsonov, D. Sorokin and M. Tonin, BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D = 6 and M 5-branes, Phys. Rev. D 80 (2009) 086008 [arXiv:0907.4596] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  39. K. Furuuchi, Non-linearly extended self-dual relations from the Nambu-Bracket description of M 5-brane in a constant c-field background, JHEP 03 (2010) 127 [arXiv:1001.2300] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. B. Czech, Y.-t. Huang and M. Rozali, Amplitudes for multiple M 5 branes, arXiv:1110.2791 [INSPIRE].

  41. S. Bolognesi and K. Lee, 1/4 BPS string junctions and N 3 problem in 6-dim (2, 0) superconformal theories, Phys. Rev. D 84 (2011) 126018 [arXiv:1105.5073] [INSPIRE].

    ADS  Google Scholar 

  42. H.-C. Kim, S. Kim, E. Koh, K. Lee and S. Lee, On instantons as Kaluza-Klein modes of M 5-branes, JHEP 12 (2011) 031 [arXiv:1110.2175] [INSPIRE].

    Article  ADS  Google Scholar 

  43. S. Terashima and F. Yagi, On effective action of multiple M 5-branes and ABJM action, JHEP 03 (2011) 036 [arXiv:1012.3961] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. H. Singh, Super-Yang-Mills and M 5-branes, JHEP 08 (2011) 136 [arXiv:1107.3408] [INSPIRE].

    Article  ADS  Google Scholar 

  45. Y. Tachikawa, On S-duality of 5D super Yang-Mills on S 1, JHEP 11 (2011) 123 [arXiv:1110.0531] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. C. Sämann and M. Wolf, On twistors and conformal field theories from six dimensions, arXiv:1111.2539 [INSPIRE].

  47. A. Gustavsson, M 5 brane on R 1,2 × S 3, JHEP 01 (2012) 057 [arXiv:1111.5392] [INSPIRE].

    Article  ADS  Google Scholar 

  48. N. Lambert, H. Nastase and C. Papageorgakis, 5D Yang-Mills instantons from ABJM monopoles, Phys. Rev. D 85 (2012) 066002 [arXiv:1111.5619] [INSPIRE].

    ADS  Google Scholar 

  49. A. Gustavsson, A preliminary test of abelian D4-M 5 duality, Phys. Lett. B 706 (2011) 225 [arXiv:1111.6339] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  50. D.S. Berman, M-theory branes and their interactions, Phys. Rept. 456 (2008) 89 [arXiv:0710.1707] [INSPIRE].

    Article  ADS  Google Scholar 

  51. P. Arvidsson, Superconformal theories in six dimensions, hep-th/0608014 [INSPIRE].

  52. M. Bañados, L.J. Garay and M. Henneaux, The local degrees of freedom of higher dimensional pure Chern-Simons theories, Phys. Rev. D 53 (1996) 593 [hep-th/9506187] [INSPIRE].

    ADS  Google Scholar 

  53. M. Bañados, L.J. Garay and M. Henneaux, The dynamical structure of higher dimensional Chern-Simons theory, Nucl. Phys. B 476 (1996) 611 [hep-th/9605159] [INSPIRE].

    Article  ADS  Google Scholar 

  54. O. Mišković, R. Troncoso and J. Zanelli, Canonical sectors of five-dimensional Chern-Simons theories, Phys. Lett. B 615 (2005) 277 [hep-th/0504055] [INSPIRE].

    ADS  Google Scholar 

  55. M.B. Green, J.H. Schwarz and E. Witten, Superstring theory. Volume 1: introduction, Cambridge University Prress, Cambridge U.K. (1987), see chapter 2.3.

  56. A.A. Tseytlin, On non-abelian generalization of Born-Infeld action in string theory, Nucl. Phys. B 501 (1997) 41 [hep-th/9701125] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  57. A.A. Tseytlin, Born-Infeld action, supersymmetry and string theory, in The many faces of the superworld, M.A. Shifman ed., World Scientific, Singapore (1999), hep-th/9908105 [INSPIRE].

  58. P. Koerber and A. Sevrin, The non-abelian D-brane effective action through order α ′4, JHEP 10 (2002) 046 [hep-th/0208044] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. E. Witten, Conformal field theory in four and six dimensions, arXiv:0712.0157 [INSPIRE].

  60. I.A. Bandos, N. Berkovits and D.P. Sorokin, Duality symmetric eleven-dimensional supergravity and its coupling to M-branes, Nucl. Phys. B 522 (1998) 214 [hep-th/9711055] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  61. N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  62. K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  63. M. Aganagic, M. Mariño and C. Vafa, All loop topological string amplitudes from Chern-Simons theory, Commun. Math. Phys. 247 (2004) 467 [hep-th/0206164] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  64. A. Iqbal and A.-K. Kashani-Poor, SU(N ) geometries and topological string amplitudes, Adv. Theor. Math. Phys. 10 (2006) 1 [hep-th/0306032] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  65. Y. Tachikawa, Five-dimensional Chern-Simons terms and Nekrasov’s instanton counting, JHEP 02 (2004) 050 [hep-th/0401184] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  66. C.-S. Chu, work in progress.

  67. J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  68. J. Bagger and N. Lambert, Comments on multiple M2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  69. A. Gustavsson, Algebraic structures on parallel M 2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  70. T. Banks, W. Fischler, S. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  71. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  72. W. Taylor, M(atrix) theory: matrix quantum mechanics as a fundamental theory, Rev. Mod. Phys. 73 (2001) 419 [hep-th/0101126] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  73. M.R. Douglas, D-branes and matrix theory in curved space, Nucl. Phys. Proc. Suppl. 68 (1998) 381 [hep-th/9707228] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  74. M.R. Douglas, A. Kato and H. Ooguri, D-brane actions on Kähler manifolds, Adv. Theor. Math. Phys. 1 (1998) 237 [hep-th/9708012] [INSPIRE].

    MathSciNet  Google Scholar 

  75. M. Hanada, H. Kawai and Y. Kimura, Describing curved spaces by matrices, Prog. Theor. Phys. 114 (2006) 1295 [hep-th/0508211] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  76. I.R. Klebanov and A.A. Tseytlin, Entropy of near extremal black p-branes, Nucl. Phys. B 475 (1996) 164 [hep-th/9604089] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Particle Theory and Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, U.K.

    Chong-Sun Chu & Sheng-Lan Ko

Authors
  1. Chong-Sun Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng-Lan Ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sheng-Lan Ko.

Additional information

ArXiv ePrint: 1203.4224

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chu, CS., Ko, SL. Non-abelian action for multiple five-branes with self-dual tensors. J. High Energ. Phys. 2012, 28 (2012). https://doi.org/10.1007/JHEP05(2012)028

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2012)028

Keywords

Search

Navigation