Off-Shell Hodge Dualities in Linearised Gravity and E11

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 E11 and are associated with null and imaginary roots.

33 pages, 2 figures, nomenclature changed and comments added to the conclusions

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Cited by in corpus (19)

• Beyond E11
• A master exceptional field theory
• Dual Double Field Theory
• On supersymmetric E11 exceptional field theory
• E8 duality and dual gravity
• Mixed-symmetry multiplets and higher-spin curvatures
• A note on the double dual graviton
• Exotic Dual of Type II Double Field Theory
• Relation between standard and exotic duals of differential forms
• Higher spins from exotic dualisations
• A unified approach to standard and exotic dualizations through graded geometry
• Duality and higher Buscher rules in p-form gauge theory and linearized gravity
• Prepotentials for linearized supergravity
• Conserved asymptotic charges for any massless particle
• Higher dualisations of linearised gravity and the $A_1^{+++}$ algebra
• Unfolding $E_{11}$
• Gravitational Coset Models
• Gauge fields and infinite chains of dualities
• Aspects of electric-magnetic dualities in maximal supergravity