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Off-Shell Hodge Dualities in Linearised Gravity and E11
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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 E11 and are associated with null and imaginary roots.
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A unified approach to standard and exotic dualizations through graded geometry
A single two-parameter first-order action in graded geometry generates the known standard, exotic and double dualizations for p-forms and (p,1) mixed-symmetry tensors such as the graviton and Curtright field.
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