Generalized E(7(7)) coset dynamics and D=11 supergravity

TL;DR

The paper develops a manifestly off-shell $E_{7(7)}$-invariant framework in a $4+56$ dimensional setting (exceptional geometry) and derives the bosonic and fermionic dynamics for the $56$-state sector. By enforcing a hidden $ extit{Diff}(7)$ symmetry and using a Weyl rescaling with four additional dimensions, the authors show exact agreement with the bosonic and fermionic sectors of $D=11$ supergravity in the seven-dimensional truncation. They introduce a complete generalized coset dynamics for $E_{7(7)}$ and connect it to a sixty-dimensional exceptional geometry, offering a geometric interpretation and situating the construction in the broader context of hidden duality and diffeomorphism symmetries. The work suggests that exceptional geometry could underpin manifestly symmetry-enhanced formulations of lower-dimensional supergravities and potentially point toward larger duality structures such as $E_{8(8)}$, $E_{10}$, and $E_{11}$.

Abstract

The hidden on-shell E(7(7)) symmetry of maximal supergravity is usually discussed in a truncation from D=11 to four dimensions. In this article, we reverse the logic and start from a theory with manifest off-shell E(7(7)) symmetry inspired by West's coset construction. Following de Wit's and Nicolai's idea that a 4+56 dimensional "exceptional geometry" underlies maximal supergravity, we construct the corresponding Lagrangian and the supersymmetry variations for the 56 dimensional subsector. We prove that both the dynamics and the supersymmetry coincide with D=11 supergravity in a truncation to d=7 in the expected way.