exceptional structures, exceptional isomorphisms
exceptional finite rotation groups:
and Kac-Moody groups:
abstract duality: opposite category,
concrete duality: dual object, dualizable object, fully dualizable object, dualizing object
between higher geometry/higher algebra
Langlands duality, geometric Langlands duality, quantum geometric Langlands duality
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
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).
exceptional generalized geometry, exceptional tangent bundle
generalized Scherk-Schwarz reduction, gauged supergravity, tensor hierarchy, embedding tensor
Precursors include
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)
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 includes
Generalization to exceptional super-spacetimes:
Last revised on June 18, 2020 at 04:43:10. See the history of this page for a list of all contributions to it.