Generalised geometry from the ground up

Extending previous work on generalised geometry, we explicitly construct an E7(7)-valued vielbein in eleven dimensions that encompasses the would be scalar bosonic degrees of freedom after reduction to four dimensions of D = 11 supergravity, by identifying new “generalised vielbeine” in eleven dimensions associated with the dual 6-form potential and the dual graviton. By maintaining full on-shell equivalence with the original theory at every step our construction furnishes the non-linear ansatz for the dual (magnetic) 7-form flux for any non-trivial compactification of D = 11 supergravity, complementing the known non-linear ansätze for the metric and the 4-form flux. A preliminary analysis of the generalised vielbein postulate for the new vielbein components reveals tantalising hints of new structures beyond D = 11 supergravity and ordinary space-time covariancxe, and also points to the possible D = 11 origins of the embedding tensor. We discuss the extension of these results to E8(8).