An exceptional geometry for d=11 supergravity?

TL;DR

This paper explores a novel geometric structure in eleven-dimensional supergravity, demonstrating that its bosonic fields can be organized into an E_8-valued vielbein, hinting at a unification of symmetries.

Contribution

It shows that the bosonic degrees of freedom in d=11 supergravity can be assembled into an E_8-valued vielbein, revealing a new geometric perspective.

Findings

Bosonic fields form an E_8-valued vielbein in eleven dimensions

Maximal nilpotent subalgebra of E_8 plays a key role

Suggests partial unification of coordinate and gauge transformations

Abstract

We analyze the algebraic constraints of the generalized vielbein in SO(1,2) x SO(16) invariant d=11 supergravity, and show that the bosonic degrees of freedom of d=11 supergravity, which become the physical ones upon reduction to d=3, can be assembled into an E_8-valued vielbein already in eleven dimensions. A crucial role in the construction is played by the maximal nilpotent commuting subalgebra of E_8, of dimension 36, suggesting a partial unification of general coordinate and tensor gauge transformations.