Advertisement

Counterterms vs. dualities

  • Guillaume Bossard
  • Hermann Nicolai
Open Access
Article

Abstract

We investigate and clarify the mutual compatibility of the higher order corrections arising in supergravity and string theory effective actions and the non-linear duality symmetries of these theories. Starting from a conventional tree level action leading to duality invariant equations of motion, we show how to accommodate duality invariant counterterms given as functionals of both electric and magnetic fields in a perturbative expansion, and to deduce from them a non-polynomial bona fide action satisfying the Gaillard-Zumino (NGZ)constraint. There exists a corresponding consistency constraint in the non-covariant Henneaux-Teitelboim formalism which ensures that one can always restore diffeomorphism invariance by perturbatively solving this functional identity. We illustrate how this procedure works for the R 2FF and F 4 counterterms in Maxwell theory.

Keywords

Supersymmetry and Duality Extended Supersymmetry Supergravity Models Anomalies in Field and String Theories 

References

  1. [1]
    E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  2. [2]
    M.K. Gaillard and B. Zumino, Duality rotations for interacting fields, Nucl. Phys. B 193 (1981) 221 [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  3. [3]
    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].ADSGoogle Scholar
  4. [4]
    R. Kallosh, E 7(7) symmetry and finiteness of N =8 supergravity, arXiv:1103.4115 [SPIRES].
  5. [5]
    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].CrossRefADSMathSciNetGoogle Scholar
  6. [6]
    C. Hillmann, E 7(7) invariant lagrangian of D =4 N =8 supergravity, JHEP 04 (2010) 010 [arXiv:0911.5225] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  7. [7]
    P.S. Howe and U. Lindström, Higher order invariants in extended supergravity, Nucl. Phys. B 181 (1981) 487 [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    R.E. Kallosh, Counterterms in extended supergravities, Phys. Lett. B 99 (1981) 122 [SPIRES].ADSMathSciNetGoogle Scholar
  9. [9]
    P.S. Howe, K.S. Stelle and P.K. Townsend, Superactions, Nucl. Phys. B 191 (1981) 445 [SPIRES].CrossRefADSGoogle Scholar
  10. [10]
    R. Kallosh, N =8 counterterms and E 7(7) current conservation, JHEP 06 (2011) 073 [arXiv:1104.5480] [SPIRES].CrossRefADSGoogle Scholar
  11. [11]
    D.Z. Freedman and E. Tonni, The D 2k R 4 invariants of N =8 supergravity, JHEP 04 (2011) 006 [arXiv:1101.1672] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    H. Elvang and M. Kiermaier, Stringy KLT relations, global symmetries and E 7(7) violation, JHEP 10 (2010) 108 [arXiv:1007.4813] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  13. [13]
    G. Bossard, P.S. Howe and K.S. Stelle, On duality symmetries of supergravity invariants, JHEP 01 (2011) 020 [arXiv:1009.0743] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  14. [14]
    M.B. Green, J.G. Russo and P. Vanhove, Automorphic properties of low energy string amplitudes in various dimensions, Phys. Rev. D 81 (2010) 086008 [arXiv:1001.2535] [SPIRES].ADSMathSciNetGoogle Scholar
  15. [15]
    B. de Wit and H. Nicolai, N =8 supergravity, Nucl. Phys. B 208 (1982) 323 [SPIRES].CrossRefADSGoogle Scholar
  16. [16]
    M. Henneaux and C. Teitelboim, Dynamics of chiral (selfdual) p-forms, Phys. Lett. B 206 (1988) 650 [SPIRES].ADSGoogle Scholar
  17. [17]
    G. Barnich, F. Brandt and M. Henneaux, Local BRST cohomology in the antifield formalism. 1. General theorems, Commun. Math. Phys. 174 (1995) 57 [hep-th/9405109] [SPIRES].CrossRefzbMATHADSMathSciNetGoogle Scholar
  18. [18]
    L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [SPIRES].CrossRefADSGoogle Scholar
  19. [19]
    O. Alvarez, I.M. Singer and B. Zumino, Gravitational anomalies and the family’s index theorem, Commun. Math. Phys. 96 (1984) 409 [SPIRES].CrossRefzbMATHADSMathSciNetGoogle Scholar
  20. [20]
    Z. Bern, J.J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The ultraviolet behavior of N =8 supergravity at four loops, Phys. Rev. Lett. 103 (2009) 081301 [arXiv:0905.2326] [SPIRES].CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2011

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

Authors and Affiliations

  1. 1.Centre de Physique ThéoriqueEcole Polytechnique, CNRSPalaiseau CedexFrance
  2. 2.AEI, Max-Planck-Institut für GravitationsphysikPotsdamGermany

Personalised recommendations