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On duality symmetries of supergravity invariants

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Abstract

The role of duality symmetries in the construction of counterterms for maximal supergravity theories is discussed in a field-theoretic context from different points of view. These are: dimensional reduction, the question of whether appropriate superspace measures exist and information about non-linear invariants that can be gleaned from linearised ones. The former allows us to prove that F-term counterterms cannot be E 7(7)-invariant in D = 4, N = 8 supergravity or E 6(6)-invariant in D = 5 maximal supergravity. This is confirmed by the two other methods which can also be applied to D = 4 theories with fewer supersymmetries and allow us to prove that N = 6 supergravity is finite at three and four loops and that N = 5 supergravity is three-loop finite.

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Authors and Affiliations

  1. AEI, Max Planck Institut für Gravitationsphysik Am Mühlenberg 1, D-14476, Potsdam, Germany

    G. Bossard

  2. Department of Mathematics, King’s College, University of London Strand, London, WC2R 2LS, U.K.

    P. S. Howe

  3. Theoretical Physics Group, Imperial College London Prince Consort Road, London, SW7 2AZ, U.K.

    K. S. Stelle

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  1. G. Bossard
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  2. P. S. Howe
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  3. K. S. Stelle
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Correspondence to G. Bossard.

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ArXiv ePrint: 1009.0743

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Bossard, G., Howe, P.S. & Stelle, K.S. On duality symmetries of supergravity invariants. J. High Energ. Phys. 2011, 20 (2011). https://doi.org/10.1007/JHEP01(2011)020

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