E$_8$ in $\mathcal N=8$ supergravity in four dimensions

TL;DR

This paper demonstrates that four-dimensional $ =8$ supergravity possesses an exceptional $E_{8(8)}$ symmetry, which is an enhancement from the previously known $E_{7(7)}$, through a process involving dimensional reduction and field redefinition.

Contribution

The paper introduces a novel method to reveal the $E_{8(8)}$ symmetry in $ =8$ supergravity by dimensional reduction and redefinition, extending the known symmetry structure.

Findings

Identification of $E_{8(8)}$ symmetry in 4D supergravity

Method involving reduction to 3D and redefinition to make symmetry manifest

Extension of known symmetry from $E_{7(7)}$ to $E_{8(8)}$

Abstract

We argue that $\mathcal N=8$ supergravity in four dimensions exhibits an exceptional $E_{8(8)}$ symmetry, enhanced from the known $E_{7(7)}$ invariance. Our procedure to demonstrate this involves dimensional reduction of the $\mathcal N=8$ theory to $d=3$, a field redefinition to render the $E_{8(8)}$ invariance manifest, followed by dimensional oxidation back to $d=4$.