E11, generalised space-time and equations of motion in four dimensions

Abstract

We construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at low levels in four dimensions. We include the fields for gravity, the scalars and the gauge fields as well as the duals of these fields. The generalised space-time, upon which the fields depend, consists of the usual coordinates of four dimensional space-time and Lorentz scalar coordinates which belong to the 56-dimensional representation of E7. We demand that the equations of motion are first order in derivatives of the generalised space-time and then show that they are essentially uniquely determined by the properties of the E11 Kac-Moody algebra and its first fundamental representation. The two lowest equations correctly describe the equations of motion of the scalars and the gauge fields once one takes the fields to depend only on the usual four dimensional space-time.

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Cited by in corpus (25)

• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• The Geometry, Branes and Applications of Exceptional Field Theory
• E11 in 11D
• U-duality extension of Drinfel'd double
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Non-Abelian U-duality for membrane
• Weaving the Exotic Web
• E11 must be a symmetry of strings and branes
• Branes in Extended Spacetime: Brane Worldvolume Theory Based on Duality Symmetry
• A brief review of E theory
• Timelike U-dualities in Generalised Geometry
• Membrane Duality Revisited
• Generalised Space-time and Gauge Transformations
• Exceptional geometry and Borcherds superalgebras
• Exceptional M-brane sigma models and $\eta$-symbols
• Generalised vielbeins and non-linear realisations
• Born sigma model for branes in exceptional geometry
• E11 and exceptional field theory
• Dual gravity and E11
• An E11 invariant gauge fixing
• Extended Drinfel'd algebras and non-Abelian duality
• Unfolding $E_{11}$
• Reductions of Exceptional Field Theories
• Exotic branes and mixed-symmetry potentials I: predictions from $E_{11}$ symmetry
• Half-maximal Extended Drinfel'd Algebras