Exceptional versus superPoincaré algebra as the defining symmetry of maximal supergravity

Abstract

We describe how one may use either the superPoincaré algebra or the exceptional algebra to construct maximal supergravity theories in the light-cone formalism. The d = 4 construction shows both symmetries albeit in a non-linearly realized manner. In d = 11, we find that we have to choose which of these two symmetries to use, in constructing the theory. In order to understand the other “unused” symmetry, one has to perform a highly non-trivial field redefinition. We argue that this shows that one cannot trust counterterm arguments that do not take the full symmetry of the theory into account. Finally we discuss possible consequences for Superstring theory and M-theory.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  2. [2]

    E. Cremmer, B. Julia and J. Scherk, Supergravity Theory in Eleven-Dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].

    ADS  Article  Google Scholar 

  3. [3]

    L. Brink and P.S. Howe, The N = 8 Supergravity in Superspace, Phys. Lett. B 88 (1979) 268 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  4. [4]

    P.S. Howe and U. Lindström, Higher Order Invariants in Extended Supergravity, Nucl. Phys. B 181 (1981) 487 [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    Z. Bern, J.J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, Amplitudes and Ultraviolet Behavior of N = 8 Supergravity, Fortsch. Phys. 59 (2011) 561 [arXiv:1103.1848] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  6. [6]

    A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic Interaction Terms for Arbitrarily Extended Supermultiplets, Nucl. Phys. B 227 (1983) 41 [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    S. Ananth, L. Brink, R. Heise and H.G. Svendsen, The N = 8 Supergravity Hamiltonian as a Quadratic Form, Nucl. Phys. B 753 (2006) 195 [hep-th/0607019] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  8. [8]

    L. Brink, S.-S. Kim and P. Ramond, E 7(7) on the Light Cone, JHEP 06 (2008) 034 [arXiv:0801.2993] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  9. [9]

    L. Brink, O. Lindgren and B.E.W. Nilsson, N = 4 Yang-Mills Theory on the Light Cone, Nucl. Phys. B 212 (1983) 401 [INSPIRE].

    ADS  Article  Google Scholar 

  10. [10]

    S. Ananth, L. Brink and P. Ramond, Eleven-dimensional supergravity in light-cone superspace, JHEP 05 (2005) 003 [hep-th/0501079] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  11. [11]

    O. Hohm and H. Samtleben, Exceptional field theory. II. E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].

  12. [12]

    A. Coimbra, C. Strickland-Constable and D. Waldram, \( {E_d}_{(d)}\times {\mathbb{R}}^{+} \) generalised geometry, connections and M-theory, JHEP 02 (2014) 054 [arXiv:1112.3989] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  13. [13]

    H. Godazgar, M. Godazgar and H. Nicolai, Generalised geometry from the ground up, JHEP 02 (2014) 075 [arXiv:1307.8295] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  14. [14]

    H. Godazgar, M. Godazgar and H. Nicolai, Einstein-Cartan Calculus for Exceptional Geometry, JHEP 06 (2014) 021 [arXiv:1401.5984] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  15. [15]

    B. de Wit and H. Nicolai, Hidden Symmetry in d = 11 Supergravity, Phys. Lett. B 155 (1985) 47 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  16. [16]

    B. de Wit and H. Nicolai, d = 11 Supergravity With Local SU(8) Invariance, Nucl. Phys. B 274 (1986) 363 [INSPIRE].

  17. [17]

    N. Marcus and J.H. Schwarz, Three-Dimensional Supergravity Theories, Nucl. Phys. B 228 (1983) 145 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  18. [18]

    H. Nicolai, D = 11 Supergravity With Local SO(16) Invariance, Phys. Lett. B 187 (1987) 316 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  19. [19]

    L. Brink, S.-S. Kim and P. Ramond, E 8(8) in Light Cone Superspace, JHEP 07 (2008) 113 [arXiv:0804.4300] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  20. [20]

    A.K.H. Bengtsson, L. Brink and S.-S. Kim, Counterterms in Gravity in the Light-Front Formulation and a D = 2 Conformal-like Symmetry in Gravity, JHEP 03 (2013) 118 [arXiv:1212.2776] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  21. [21]

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

  22. [22]

    S. Ananth, L. Brink and P. Ramond, Oxidizing super Yang-Mills from (N = 4, d = 4) to (N = 1, d = 10), JHEP 07 (2004) 082 [hep-th/0405150] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  23. [23]

    B. Julia, Kac-Moody Symmetry Of Gravitation And Supergravity Theories, LPTENS-82-22 C82-07-06 [INSPIRE].

  24. [24]

    P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  25. [25]

    T. Damour, M. Henneaux and H. Nicolai, E 10 and a ‘small tension expansion’ of M-theory, Phys. Rev. Lett. 89 (2002) 221601 [hep-th/0207267] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  26. [26]

    T. Damour, A. Kleinschmidt and H. Nicolai, Hidden symmetries and the fermionic sector of eleven-dimensional supergravity, Phys. Lett. B 634 (2006) 319 [hep-th/0512163] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  27. [27]

    L. Brink, P. Di Vecchia and P.S. Howe, A Locally Supersymmetric and Reparametrization Invariant Action for the Spinning String, Phys. Lett. B 65 (1976) 471 [INSPIRE].

    ADS  Article  Google Scholar 

  28. [28]

    S. Deser and B. Zumino, A Complete Action for the Spinning String, Phys. Lett. B 65 (1976) 369 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sudarshan Ananth.

Additional information

ArXiv ePrint: 1601.02836

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ananth, S., Brink, L. & Majumdar, S. Exceptional versus superPoincaré algebra as the defining symmetry of maximal supergravity. J. High Energ. Phys. 2016, 51 (2016). https://doi.org/10.1007/JHEP03(2016)051

Download citation

Keywords

  • Extended Supersymmetry
  • Space-Time Symmetries
  • Supergravity Models
  • Field Theories in Higher Dimensions