Generalised geometry from the ground up

TL;DR

This paper constructs an E7-valued vielbein in eleven dimensions for D=11 supergravity, incorporating dual potentials and avoiding typical constraints, revealing new structures and potential origins of the embedding tensor.

Contribution

It explicitly constructs a generalized vielbein in eleven dimensions that includes dual potentials, avoiding constraints and providing a new non-linear flux ansatz.

Findings

Constructed E7-valued vielbein encompassing dual potentials.

Avoided constraints typical in other generalized geometry approaches.

Provided a non-linear ansatz for dual 7-form flux.

Abstract

Extending previous work on generalised geometry, we explicitly construct an E7-valued vielbein in eleven dimensions that encompasses the scalar bosonic degrees of freedom 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 altogether avoids the constraints usually encountered in other approaches to generalised geometry and, as a side product, also 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 ansaetze 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 covariance, and also points to the possible D=11 origins of the embedding tensor. We discuss the extension of these results to E8.