Exceptional Form of D=11 Supergravity

TL;DR

This paper extends eleven-dimensional supergravity to be fully covariant under exceptional groups E_{n(n)} (n=6,7,8), revealing a geometric origin for the symmetries associated with M-theory and U-duality.

Contribution

It introduces an exceptional spacetime framework that makes D=11 supergravity covariant under E_{n(n)} groups, unifying various supergravity theories without truncation.

Findings

Explicit E_{6(6)} covariant form of D=11 supergravity

Embedding of full supergravity into a 5+27 dimensional theory

Proposes that the covariant form includes type IIB supergravity

Abstract

Eleven-dimensional supergravity reveals large exceptional symmetries upon reduction, in accordance with the U-duality groups of M-theory, but their higher-dimensional geometric origin has remained a mystery. In this letter, we show that D=11 supergravity can be extended to be fully covariant under the exceptional groups E_{n(n)}, n=6,7,8. Motivated by a similar formulation of double field theory we introduce an extended `exceptional spacetime'. We illustrate the construction by giving the explicit E_{6(6)} covariant form: the full D=11 supergravity, in a 5+6 splitting of coordinates but without truncation, embeds into an E_{6(6)} covariant 5+27 dimensional theory. We argue that this covariant form likewise comprises type IIB supergravity.