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Off-shell Hodge dualities in linearised gravity and E 11

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Abstract

In a spacetime of dimension n, the dual graviton is characterised by a Young diagram with two columns, the first of length n − 3 and the second of length one. In this paper we perform the off-shell dualisation relating the dual graviton to the double-dual graviton, displaying the precise off-shell field content and gauge invariances. We then show that one can further perform infinitely many off-shell dualities, reformulating linearised gravity in an infinite number of equivalent actions. The actions require supplementary mixed-symmetry fields which are contained within the generalised Kac-Moody algebra E 11 and are associated with null and imaginary roots.

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Authors and Affiliations

  1. Service de Mécanique et Gravitation, Université de Mons — UMONS, 20 Place du Parc, 7000, Mons, Belgium

    Nicolas Boulanger & Dmitry Ponomarev

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

    Paul. P. Cook

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  1. Nicolas Boulanger
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Correspondence to Nicolas Boulanger.

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ArXiv ePrint: 1205.2277

Research Associate of the Fund for Scientific Research-FNRS (Belgium). (Nicolas Boulanger)

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Boulanger, N., Cook, P.P. & Ponomarev, D. Off-shell Hodge dualities in linearised gravity and E 11 . J. High Energ. Phys. 2012, 89 (2012). https://doi.org/10.1007/JHEP09(2012)089

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