Contents

duality

# Contents

## Idea

In the context of supergravity and string theory, the term exceptional field theory has come to be used for formulations of 11-dimensional supergravity which make the (exceptional, whence the name) U-duality symmetry group structure manifest. This is in generalization of the “double field theory” formulation of 10d type II supergravity which makes (only) the T-duality symmetry manifest.

Accordingly, exceptional field theory is related to exceptional generalized geometry as double field theory is related to generalized complex geometry.

A spacetime in exceptional field theory is locally modeled on the Cartesian product

$\mathbb{R}^{1,d-1} \times R$

of a $d$-dimensional Minkowski space with the fundamental representation vector space $R$ of a form of the exceptional Lie group $E_{11-d}$ (the U-duality group). In the literature the former is called external space and the latter internal space. Fields on this spacetime are subject to satisfy a certain differential equation derived from an invariant form of the representation and one considers a generalized isometry algebra on this space which fails the Jacobi identity by a term proportional to this contraint (e.g. Baguet-Hohm-Samtleben 15, section 2).

## References

Precursors include

The original articles are

For a complete review of exceptional field theory see

Review for KK-compactification to 5d supergravity, hence for E6-U-duality, includes

Discussion of solitonic black brane (and exotic brane) solutions in terms of EFT includes

Discussion for E11:

Discussion for E9:

Generalization to exceptional super-spacetimes: