E11, Romans theory and higher level duality relations

Abstract

From the underlying non-linear realisation we compute the complete E11 invariant equations of motion in eleven dimensions, at the linearised level, up to and including level four in the fields. Thus we include the metric, the three and six forms, the dual graviton and three fields at level four. The fields are linked by a set of duality equations, which are first order in derivatives and transform into each other under the E11 symmetries. From these duality relations we deduce second order equations of motion, including those for the usual supergravity fields. As a result the on-shell degrees of freedom are those of the eleven dimensional supergravity. We also show that the level four fields provide an eleven dimensional origin of Romans theory and lead to a novel duality relation.

29 pages, a note has been added that contains further E11 variations of the level four fields

References in corpus (21)

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Cited by in corpus (13)

• Beyond E11
• A master exceptional field theory
• On supersymmetric E11 exceptional field theory
• On the different formulations of the E11 equations of motion
• The non-linear dual gravity equation of motion in eleven dimensions
• E11 and the non-linear dual graviton
• Irreducible representations of E theory
• Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
• Quantum Supersymmetric Cosmological Billiards and their Hidden Kac-Moody Structure
• Gravity, Dual Gravity and A1+++
• E theory in seven dimensions
• Unfolding $E_{11}$
• Kac-Moody algebras and the cosmological constant