The E(11) origin of all maximal supergravities - the hierarchy of field-strengths

TL;DR

This paper derives the structure of all maximal gauged supergravity theories across dimensions from the $E_{11}$ algebra, unifying their bosonic sectors and deformations through a single tensor related to the embedding tensor.

Contribution

It presents a unified algebraic framework based on $E_{11}$ for deriving all maximal gauged supergravities and their deformations in any dimension.

Findings

All deformations are uniquely determined by a single tensor.

The hierarchy of fields in $E_{11}$ is crucial for derivation.

Provides a unified derivation of bosonic sectors of supergravities.

Abstract

Starting from $E_{11}$ and the space-time translations we construct an algebra that promotes the global $E_{11}$ symmetries to local ones, and consider all its possible massive deformations. The Jacobi identities imply that such deformations are uniquely determined by a single tensor that belongs to the same representation of the internal symmetry group as the $D-1$ forms specified by $E_{11}$. The non-linear realisation of the deformed algebra gives the field strengths of the theory which are those of any possible gauged maximal supergravity theory in any dimension. All the possible deformed algebras are in one to one correspondence with all the possible massive maximal supergravity theories. The hierarchy of fields inherent in the $E_{11}$ formulation plays an important role in the derivation. The tensor that determines the deformation can be identified with the embedding tensor used previously to parameterise gauged supergravities. Thus we provide a very efficient, simple and unified derivation of the bosonic sector, and in the absence of gravity, of all maximal gauged supergravities from $E_{11}$.