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The M5-brane action revisited

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Abstract

We construct an alternative form of the M5-brane action in which the sixdimensional worldvolume is subject to a covariant split into 3+3 directions by a triplet of auxiliary fields. We consider the relation of this action to the original form of the M5-brane action and to a Nambu-Poisson 5-brane action based on the Bagger-Lambert-Gustavsson model with the gauge symmetry of volume preserving diffeomorphisms.

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References

  1. D. Zwanziger, Local lagrangian quantum field theory of electric and magnetic charges, Phys. Rev. D 3 (1971) 880 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  2. S. Deser and C. Teitelboim, Duality transformations of abelian and nonabelian gauge fields, Phys. Rev. D 13 (1976) 1592 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. R. Kallosh, N = 8 counterterms and E 7(7) current conservation, JHEP 06 (2011) 073 [arXiv:1104.5480] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. G. Bossard and H. Nicolai, Counterterms vs. dualities, JHEP 08 (2011) 074 [arXiv:1105.1273] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. J.J.M. Carrasco, R. Kallosh and R. Roiban, Covariant procedures for perturbative non-linear deformation of duality-invariant theories, Phys. Rev. D 85 (2012) 025007 [arXiv:1108.4390] [INSPIRE].

    ADS  Google Scholar 

  6. W. Chemissany, R. Kallosh and T. Ortín, Born-Infeldl with higher derivatives, Phys. Rev. D 85 (2012) 046002 [arXiv:1112.0332] [INSPIRE].

    ADS  Google Scholar 

  7. P. Pasti, D. Sorokin and M. Tonin, Covariant actions for models with non-linear twisted self-duality, Phys. Rev. D 86 (2012) 045013 [arXiv:1205.4243] [INSPIRE].

    ADS  Google Scholar 

  8. R. Roiban and A. Tseytlin, On duality symmetry in perturbative quantum theory, JHEP 10 (2012) 099 [arXiv:1205.0176] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. S.M. Kuzenko, Nonlinear self-duality in N = 2 supergravity, JHEP 06 (2012) 012 [arXiv:1202.0126] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. E. Ivanov and B. Zupnik, Bispinor auxiliary fields in duality-invariant electrodynamics revisited, Phys. Rev. D 87 (2013) 065023 [arXiv:1212.6637] [INSPIRE].

    ADS  Google Scholar 

  11. E. Witten, Some comments on string dynamics, hep-th/9507121 [INSPIRE].

  12. 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 

  13. N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, M5-branes, D4-branes and quantum 5D super-Yang-Mills, JHEP 01 (2011) 083 [arXiv:1012.2882] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. 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 

  15. H. Singh, Super-Yang-Mills and M5-branes, JHEP 08 (2011) 136 [arXiv:1107.3408] [INSPIRE].

    Article  ADS  Google Scholar 

  16. N. Lambert and P. Richmond, (2, 0) supersymmetry and the light-cone description of M5-branes, JHEP 02 (2012) 013 [arXiv:1109.6454] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, Deconstructing (2, 0) proposals, Phys. Rev. D 88 (2013) 026007 [arXiv:1212.3337] [INSPIRE].

    ADS  Google Scholar 

  18. 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 

  19. K.-W. Huang, Non-abelian chiral 2-form and M5-branes, arXiv:1206.3983 [INSPIRE].

  20. C.-S. Chu and S.-L. Ko, Non-abelian action for multiple five-branes with self-dual tensors, JHEP 05 (2012) 028 [arXiv:1203.4224] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. C.-S. Chu, S.-L. Ko and P. Vanichchapongjaroen, Non-abelian self-dual string solutions, JHEP 09 (2012) 018 [arXiv:1207.1095] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. C.-S. Chu and P. Vanichchapongjaroen, Non-abelian self-dual string and M2-M5 branes intersection in supergravity, JHEP 06 (2013) 028 [arXiv:1304.4322] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  23. F. Bonetti, T.W. Grimm and S. Hohenegger, A Kaluza-Klein inspired action for chiral p-forms and their anomalies, Phys. Lett. B 720 (2013) 424 [arXiv:1206.1600] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. F. Bonetti, T.W. Grimm and S. Hohenegger, Non-abelian tensor towers and (2, 0) superconformal theories, JHEP 05 (2013) 129 [arXiv:1209.3017] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  25. H. Singh, The Yang-Mills and chiral fields in six dimensions, JHEP 02 (2013) 056 [arXiv:1211.3281] [INSPIRE].

    Article  ADS  Google Scholar 

  26. H.-C. Kim and K. Lee, Supersymmetric M5 brane theories on R × CP2, JHEP 07 (2013) 072 [arXiv:1210.0853] [INSPIRE].

    Article  ADS  Google Scholar 

  27. D. Fiorenza, H. Sati and U. Schreiber, Multiple M5-branes, string 2-connections and 7D nonabelian Chern-Simons theory, arXiv:1201.5277 [INSPIRE].

  28. C. Sämann and M. Wolf, Non-abelian tensor multiplet equations from twistor space, arXiv:1205.3108 [INSPIRE].

  29. C. Sämann, M-brane models and loop spaces, Mod. Phys. Lett. A 27 (2012) 1230019 [arXiv:1206.0432] [INSPIRE].

    Article  Google Scholar 

  30. S. Palmer and C. Sämann, M-brane models from non-abelian gerbes, JHEP 07 (2012) 010 [arXiv:1203.5757] [INSPIRE].

    Article  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  MathSciNet  ADS  Google Scholar 

  32. I. Bandos, H. Samtleben and D. Sorokin, Duality-symmetric actions for non-abelian tensor fields, Phys. Rev. D 88 (2013) 025024 [arXiv:1305.1304] [INSPIRE].

    ADS  Google Scholar 

  33. C. Sämann and M. Wolf, Six-dimensional superconformal field theories from principal 3-bundles over twistor space, arXiv:1305.4870 [INSPIRE].

  34. C.-S. Chu and H. Isono, Instanton string and M-wave in multiple M5-branes system, arXiv:1305.6808 [INSPIRE].

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

    Article  MathSciNet  ADS  Google Scholar 

  36. 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].

    Article  MathSciNet  ADS  Google Scholar 

  37. D.P. Sorokin, V. Tkach and D. Volkov, Superparticles, twistors and siegel symmetry, Mod. Phys. Lett. A 4 (1989) 901 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. I.A. Bandos, D.P. Sorokin, M. Tonin, P. Pasti and D.V. Volkov, Superstrings and supermembranes in the doubly supersymmetric geometrical approach, Nucl. Phys. B 446 (1995) 79 [hep-th/9501113] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. D.P. Sorokin, Superbranes and superembeddings, Phys. Rept. 329 (2000) 1 [hep-th/9906142] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. I.A. Bandos, Superembedding approach to Dp-branes, M-branes and multiple D(0)-brane systems, Phys. Part. Nucl. Lett. 8 (2011) 149 [arXiv:0912.2530] [INSPIRE].

    Article  Google Scholar 

  41. 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 

  42. 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 

  43. J.H. Schwarz and A. Sen, Duality symmetric actions, Nucl. Phys. B 411 (1994) 35 [hep-th/9304154] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. 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 

  45. 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 

  46. J.H. Schwarz, Coupling a selfdual tensor to gravity in six-dimensions, Phys. Lett. B 395 (1997) 191 [hep-th/9701008] [INSPIRE].

    Article  ADS  Google Scholar 

  47. 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].

    Article  MathSciNet  ADS  Google Scholar 

  48. M. Henneaux and C. Teitelboim, Consistent quantum mechanics of chiral p forms, in the proceedings of Santiago 1987. Quantum mechanics of fundamental systems, December 17–20, Santiago, Chile (1987).

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

    Article  ADS  Google Scholar 

  50. P.S. Howe, E. Sezgin and P.C. West, The six-dimensional selfdual tensor, Phys. Lett. B 400 (1997) 255 [hep-th/9702111] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. 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].

    Article  MathSciNet  ADS  Google Scholar 

  52. P. Pasti, D.P. Sorokin and M. Tonin, Note on manifest Lorentz and general coordinate invariance in duality symmetric models, Phys. Lett. B 352 (1995) 59 [hep-th/9503182] [INSPIRE].

    Article  ADS  Google Scholar 

  53. P. Pasti, D.P. Sorokin and M. Tonin, Duality symmetric actions with manifest space-time symmetries, Phys. Rev. D 52 (1995) 4277 [hep-th/9506109] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  54. A. Maznytsia, C.R. Preitschopf and D.P. Sorokin, Duality of selfdual actions, Nucl. Phys. B 539 (1999) 438 [hep-th/9805110] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. J. Bagger and N. Lambert, Modeling multiple M2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  56. 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 

  57. A. Gustavsson, Algebraic structures on parallel M2-branes, Nucl. Phys. B 811 (2009) 66 [arXiv:0709.1260] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. P.-M. Ho and Y. Matsuo, M5 from M2, JHEP 06 (2008) 105 [arXiv:0804.3629] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  60. P.-M. Ho, A concise review on M5-brane in large c-field background, Chin. J. Phys. 48 (2010) 1 [arXiv:0912.0445] [INSPIRE].

    ADS  Google Scholar 

  61. C.-H. Chen, K. Furuuchi, P.-M. Ho and T. Takimi, More on the Nambu-Poisson M5-brane theory: scaling limit, background independence and an all order solution to the Seiberg-Witten map, JHEP 10 (2010) 100 [arXiv:1006.5291] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  62. A. Gustavsson, M5 brane from mass deformed BLG theory, JHEP 11 (2009) 071 [arXiv:0909.2518] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  64. P. Pasti, I. Samsonov, D. Sorokin and M. Tonin, BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D = 6 and M5-branes, Phys. Rev. D 80 (2009) 086008 [arXiv:0907.4596] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  65. K. Furuuchi, Non-linearly extended self-dual relations from the Nambu-Bracket description of M5-brane in a constant c-field background, JHEP 03 (2010) 127 [arXiv:1001.2300] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  66. I.A. Bandos and P.K. Townsend, Light-cone M5 and multiple M2-branes, Class. Quant. Grav. 25 (2008) 245003 [arXiv:0806.4777] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  67. N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. D. Belov and G.W. Moore, Holographic action for the self-dual field, hep-th/0605038 [INSPIRE].

  69. S. Monnier, The anomaly line bundle of the self-dual field theory, arXiv:1109.2904 [INSPIRE].

  70. W.-M. Chen and P.-M. Ho, Lagrangian formulations of self-dual gauge theories in diverse dimensions, Nucl. Phys. B 837 (2010) 1 [arXiv:1001.3608] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  71. W.-H. Huang, Lagrangian of self-dual gauge fields in various formulations, Nucl. Phys. B 861 (2012) 403 [arXiv:1111.5118] [INSPIRE].

    Article  ADS  Google Scholar 

  72. 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 

  73. L. Dolan and C.R. Nappi, A modular invariant partition function for the five-brane, Nucl. Phys. B 530 (1998) 683 [hep-th/9806016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  74. M. Henningson, B.E. Nilsson and P. Salomonson, Holomorphic factorization of correlation functions in (4k + 2)-dimensional (2k) form gauge theory, JHEP 09 (1999) 008 [hep-th/9908107] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  75. E. Witten, Duality relations among topological effects in string theory, JHEP 05 (2000) 031 [hep-th/9912086] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  76. A. Sevrin and D.C. Thompson, A note on supersymmetric chiral bosons, arXiv:1305.4848 [INSPIRE].

  77. W.-M. Chen, P.-M. Ho, H.-c. Kao, F.S. Khoo and Y. Matsuo, Partition Function of Chiral Boson on 2-Torus from Floreanini-Jackiw Lagrangian, arXiv:1307.2172 [INSPIRE].

  78. M.K. Gaillard and B. Zumino, Duality rotations for interacting fields, Nucl. Phys. B 193 (1981) 221 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  79. G. Gibbons and D. Rasheed, Electric-magnetic duality rotations in nonlinear electrodynamics, Nucl. Phys. B 454 (1995) 185 [hep-th/9506035] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  80. M. Hatsuda, K. Kamimura and S. Sekiya, Electric magnetic duality invariant Lagrangians, Nucl. Phys. B 561 (1999) 341 [hep-th/9906103] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  81. P.S. Howe, N. Lambert and P.C. West, The selfdual string soliton, Nucl. Phys. B 515 (1998) 203 [hep-th/9709014] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  82. E. Bergshoeff, D. Berman, J. van der Schaar and P. Sundell, A noncommutative M-theory five-brane, Nucl. Phys. B 590 (2000) 173 [hep-th/0005026] [INSPIRE].

    Article  ADS  Google Scholar 

  83. E. Witten, Nonperturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  84. R. Kallosh and D. Sorokin, Dirac action on M5 and M2 branes with bulk fluxes, JHEP 05 (2005) 005 [hep-th/0501081] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  85. L. Anguelova and K. Zoubos, Five-brane instantons vs. flux-induced gauging of isometries, JHEP 10 (2006) 071 [hep-th/0606271] [INSPIRE].

  86. D. Tsimpis, Fivebrane instantons and Calabi-Yau fourfolds with flux, JHEP 03 (2007) 099 [hep-th/0701287] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  87. M. Kerstan and T. Weigand, Fluxed M5-instantons in F-theory, Nucl. Phys. B 864 (2012) 597 [arXiv:1205.4720] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  88. M. Bianchi, G. Inverso and L. Martucci, Brane instantons and fluxes in F-theory, JHEP 07 (2013) 037 [arXiv:1212.0024] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

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Ko, SL., Sorokin, D. & Vanichchapongjaroen, P. The M5-brane action revisited. J. High Energ. Phys. 2013, 72 (2013). https://doi.org/10.1007/JHEP11(2013)072

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