nLab exceptional field theory

Contents

Context

Exceptional structures

String theory

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

1,d1×R \mathbb{R}^{1,d-1} \times R

of a dd-dimensional Minkowski space with the fundamental representation vector space RR of a form of the exceptional Lie group E 11dE_{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

Review:

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:

Application to AdS4/CFT3:

  • Oscar Varela, Super-Chern-Simons spectra from Exceptional Field Theory (arXiv:2010.09743)

See also:

On application to KK-reduction of D=10 supergravity and D=11 supergravity on squashed 7-spheres:

Last revised on January 11, 2024 at 13:10:19. See the history of this page for a list of all contributions to it.