Skip to main content
SpringerLink
Log in

N=8 counterterms and E 7(7) current conservation

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

Abstract

We examine conservation of the E 7(7) Noether-Gaillard-Zumino current in the presence of N=8 supergravity counterterms using the momentum space helicity formalism, which significantly simplifies the calculations. The main result is that the 4-point counterterms at any loop order L are forbidden by the E 7(7) current conservation identity. We also clarify the relation between linearized and full non-linear superinvariants as candidate counterterms. This enables us to show that all n-point counterterms at L = 7, 8 are forbidden since they provide a non-linear completions of the 4-point ones. This supports and exemplifies our general proof in arXiv:1103.4115 of perturbative UV finiteness of N=8 supergravity.

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. R. Kallosh, The ultraviolet finiteness of N = 8 supergravity, JHEP 12 (2010) 009 [arXiv:1009.1135] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  2. R. Kallosh, E 7(7) symmetry and finiteness of N = 8 supergravity, arXiv:1103.4115 [SPIRES].

  3. E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  4. B. de Wit and H. Nicolai, N = 8 supergravity, Nucl. Phys. B 208 (1982) 323 [SPIRES].

    Article  ADS  Google Scholar 

  5. B. de Wit, Properties of SO(8) extended supergravity, Nucl. Phys. B 158 (1979) 189 [SPIRES].

    Article  ADS  Google Scholar 

  6. B. de Wit and D.Z. Freedman, On SO(8) extended supergravity, Nucl. Phys. B 130 (1977) 105 [SPIRES].

    Article  ADS  Google Scholar 

  7. S. Ferrara and A. Marrani, Perturbative and non-perturbative aspects of N = 8 supergravity, arXiv:1103.5138 [SPIRES].

  8. L. Brink, private communication (2011).

  9. G. Bossard, C. Hillmann and H. Nicolai, E 7(7) symmetry in perturbatively quantised N = 8 supergravity, JHEP 12 (2010) 052 [arXiv:1007.5472] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  11. S.M. Kuzenko and S. Theisen, Supersymmetric duality rotations, JHEP 03 (2000) 034 [hep-th/0001068] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. P. Aschieri, S. Ferrara and B. Zumino, Duality rotations in nonlinear electrodynamics and in extended supergravity, Riv. Nuovo Cim. 31 (2008) 625 [arXiv:0807.4039] [SPIRES].

    ADS  Google Scholar 

  13. R. Kallosh and M. Soroush, Explicit action of E 7(7) on N = 8 supergravity fields, Nucl. Phys. B 801 (2008) 25 [arXiv:0802.4106] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. P.S. Howe and U. Lindström, Higher order invariants in extended supergravity, Nucl. Phys. B 181 (1981) 487 [SPIRES].

    Article  ADS  Google Scholar 

  15. R.E. Kallosh, Counterterms in extended supergravities, Phys. Lett. B 99 (1981) 122 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  16. P.S. Howe, K.S. Stelle and P.K. Townsend, Superactions, Nucl. Phys. B 191 (1981) 445 [SPIRES].

    Article  ADS  Google Scholar 

  17. L. Brink and P.S. Howe, The N = 8 supergravity in superspace, Phys. Lett. B 88 (1979) 268 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  18. Z. Bern et al., Three-loop superfiniteness of N = 8 supergravity, Phys. Rev. Lett. 98 (2007) 161303 [hep-th/0702112] [SPIRES].

    Article  ADS  Google Scholar 

  19. J. Broedel and L.J. Dixon, R 4 counterterm and E 7(7) symmetry in maximal supergravity, JHEP 05 (2010) 003 [arXiv:0911.5704] [SPIRES].

    Article  ADS  Google Scholar 

  20. H. Elvang and M. Kiermaier, Stringy KLT relations, global symmetries and E 7(7) violation, JHEP 10 (2010) 108 [arXiv:1007.4813] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. G. Bossard, P.S. Howe and K.S. Stelle, On duality symmetries of supergravity invariants, JHEP 01 (2011) 020 [arXiv:1009.0743] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. R. Kallosh, N = 8 supergravity on the light cone, Phys. Rev. D 80 (2009) 105022 [arXiv:0903.4630] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  23. H. Elvang, D.Z. Freedman and M. Kiermaier, A simple approach to counterterms in N = 8 supergravity, JHEP 11 (2010) 016 [arXiv:1003.5018] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. N. Beisert et al., E 7(7) constraints on counterterms in N = 8 supergravity, Phys. Lett. B 694 (2010) 265 [arXiv:1009.1643] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  25. H. Elvang, D.Z. Freedman and M. Kiermaier, SUSY Ward identities, superamplitudes and counterterms, arXiv:1012.3401 [SPIRES].

  26. D.Z. Freedman and E. Tonni, The D 2k R 4 invariants of N = 8 supergravity, JHEP 04 (2011) 006 [arXiv:1101.1672] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  27. M.B. Green and P. Vanhove, The low energy expansion of the one-loop type-II superstring amplitude, Phys. Rev. D 61 (2000) 104011 [hep-th/9910056] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  28. R. Kallosh, On a possibility of a UV finite N = 8 supergravity, arXiv:0808.2310 [SPIRES].

  29. E. Sokatchev, A superspace action for N = 2 supergravity, Phys. Lett. B 100 (1981) 466 [SPIRES].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA, 94305-4060, U.S.A.

    Renata Kallosh

Authors
  1. Renata Kallosh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Renata Kallosh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kallosh, R. N=8 counterterms and E 7(7) current conservation. J. High Energ. Phys. 2011, 73 (2011). https://doi.org/10.1007/JHEP06(2011)073

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2011)073

Keywords

Search

Navigation