Counterterms vs. dualities

  • Guillaume Bossard
  • Hermann Nicolai
Open Access


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.


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


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© 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

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