An 'exceptional' form for symmetries in maximal supergravity

TL;DR

The paper argues that global symmetries of maximally supersymmetric gravity in $d\ge4$ admit a universal coset-form in light-cone superspace, tying together exceptional groups like $E_{7(7)}$ in $d=4$ and their classical counterparts in higher dimensions. It develops a general framework where the $H$-part acts linearly and the coset $K=G/H$ acts nonlinearly in a way that preserves chirality, providing explicit constructions and checks across $d=4$–$7$. The authors demonstrate that the same universal structure governs the $SU(8)$, $USp(8)$, and related R-symmetries in these dimensions and discuss an all-order approach for the $d=4$ case, as well as an oxidation procedure to obtain higher-dimensional Lagrangians. This work has implications for understanding ultraviolet properties and the interdimension connectivity of maximal supergravity via a compact, symmetry-driven formalism in light-cone superspace.

Abstract

The global symmetries in maximally supersymmetric theories of gravity in $d\ge4$ are shown to have a universal form in light-cone superspace. The procedure for deriving an all order expression for the $d=4$ case is also discussed.