nLab exceptional field theory

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).

Related concepts

• U-duality, exceptional Lie group

• exceptional generalized geometry, exceptional tangent bundle

• non-geometry, exotic branes

• double field theory

• generalized Scherk-Schwarz reduction, gauged supergravity, tensor hierarchy, embedding tensor

• exceptional geometry

• universal exceptionalism

References

Precursors include

• Olaf Hohm, Henning Samtleben, U-duality covariant gravity (arXiv:1307.0509)

The original articles are

• Olaf Hohm, Henning Samtleben, Exceptional Form of $D=11$ Supergravity, Phys. Rev. Lett. 111, 231601 (2013) (arXiv:1308.1673)

• Olaf Hohm, Henning Samtleben, Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB, Phys. Rev. D 89, 066016 (2014) (arXiv:1312.0614)

• Olaf Hohm, Henning Samtleben, Exceptional Field Theory II: $E_{7(7)}$, Phys. Rev. D 89, 066017 (2014) (arXiv:1312.4542)

• Olaf Hohm, Henning Samtleben, Exceptional Field Theory III: $E_{8(8)}$, Phys. Rev. D 90, 066002 (2014) (arXiv:1406.3348)

Review:

• David Berman, Chris D. A. Blair, The Geometry, Branes and Applications of Exceptional Field Theory, International Journal of Modern Physics A 35 30 (2020) 2030014 [arXiv:2006.09777, doi:10.1142/S0217751X20300148]

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

• Arnaud Baguet, Olaf Hohm, Henning Samtleben, $E_{6(6)}$ Exceptional Field Theory: Review and Embedding of Type IIB (arXiv:1506.01065)

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

• David Berman, Felix Rudolph, Strings, Branes and the Self-dual Solutions of Exceptional Field Theory (arXiv.1412.2768)

Discussion for E11:

• Alexander G. Tumanov, Peter West, $E_{11}$ and exceptional field theory (arXiv:1507.08912)

• Guillaume Bossard, Axel Kleinschmidt, Ergin Sezgin, On supersymmetric E11 exceptional field theory (arXiv:1907.02080)

• Guillaume Bossard, Axel Kleinschmidt, Ergin Sezgin, A master exceptional field theory (arXiv:2103.13411)

Discussion for E9:

• Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Henning Samtleben, $E_9$ exceptional field theory II. The complete dynamics (arXiv:2103.12118)

Generalization to exceptional super-spacetimes:

• Daniel Butter, Henning Samtleben, Ergin Sezgin, $E_{7(7)}$-Exceptional Field Theory in Superspace (arXiv:1811.00038)

Application to AdS4/CFT3:

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