E8 in \( \mathcal{N}=8 \) supergravity in four dimensions

Abstract

We argue that \( \mathcal{N}=8 \) supergravity in four dimensions exhibits an exceptional E8(8) symmetry, enhanced from the known E7(7) invariance. Our procedure to demonstrate this involves dimensional reduction of the \( \mathcal{N}=8 \) theory to d = 3, a field redefinition to render the E8(8) invariance manifest, followed by dimensional oxidation back to d = 4.

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].

    MathSciNet  Article  ADS  Google Scholar 

  2. [2]

    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].

  3. [3]

    S. Ananth, L. Brink and S. Majumdar, Exceptional versus superPoincaré algebra as the defining symmetry of maximal supergravity, JHEP 03 (2016) 051 [arXiv:1601.02836] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  4. [4]

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

    MathSciNet  Article  ADS  Google Scholar 

  5. [5]

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

    MathSciNet  Article  ADS  Google Scholar 

  6. [6]

    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].

  7. [7]

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

    Article  ADS  Google Scholar 

  8. [8]

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

    MathSciNet  Article  ADS  Google Scholar 

  9. [9]

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

  10. [10]

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

    Article  ADS  Google Scholar 

  11. [11]

    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].

  12. [12]

    M.B. Green, J.H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 Supergravity as Limits of String Theories, Nucl. Phys. B 198 (1982) 474 [INSPIRE].

  13. [13]

    H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  14. [14]

    S. Ananth and S. Theisen, KLT relations from the Einstein-Hilbert Lagrangian, Phys. Lett. B 652 (2007) 128 [arXiv:0706.1778] [INSPIRE].

    MathSciNet  Article  MATH  ADS  Google Scholar 

  15. [15]

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

  16. [16]

    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].

  17. [17]

    L. Brink, O. Lindgren and B.E.W. Nilsson, The Ultraviolet Finiteness of the N = 4 Yang-Mills Theory, Phys. Lett. B 123 (1983) 323.

  18. [18]

    S. Ananth, S. Kovacs and H. Shimada, Proof of all-order finiteness for planar beta-deformed Yang-Mills, JHEP 01 (2007) 046 [hep-th/0609149] [INSPIRE].

    Article  ADS  Google Scholar 

  19. [19]

    S. Ananth, S. Kovacs and H. Shimada, Proof of ultra-violet finiteness for a planar non-supersymmetric Yang-Mills theory, Nucl. Phys. B 783 (2007) 227 [hep-th/0702020] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  20. [20]

    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].

    MathSciNet  Article  MATH  ADS  Google Scholar 

  21. [21]

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

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Correspondence to Sudarshan Ananth.

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ArXiv ePrint: 1711.09110

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Ananth, S., Brink, L. & Majumdar, S. E8 in \( \mathcal{N}=8 \) supergravity in four dimensions. J. High Energ. Phys. 2018, 24 (2018). https://doi.org/10.1007/JHEP01(2018)024

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Keywords

  • Supergravity Models
  • Superspaces
  • Field Theories in Lower Dimensions