exceptional structures, exceptional isomorphisms
exceptional finite rotation groups:
and Kac-Moody groups:
exceptional Jordan superalgebra,
abstract duality: opposite category,
concrete duality: dual object, dualizable object, fully dualizable object, dualizing object
Examples
between higher geometry/higher algebra
Langlands duality, geometric Langlands duality, quantum geometric Langlands duality
In QFT and String theory
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 -dimensional Minkowski space with the fundamental representation vector space of a form of the exceptional Lie group (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 on U-duality covariant formulations of D=11 supergravity:
Bernard de Wit, Hermann Nicolai: D = 11 Supergravity With Local Invariance, Nucl. Phys. B 274, 363 (1986) [doi:10.1016/0550-3213(86)90290-7, spire:227409]
Bernard de Wit, Hermann Nicolai: Local SU(8) invariance in supergravity, talk at Nuffield Workshop on Supersymmetry and its Applications, 0357 [spire:218601]
Hermann Nicolai: On M-Theory, J Astrophys Astron 20, (1999) 149–164 [arXiv:hep-th/9801090, doi:10.1007/BF02702349]
(the term “exceptional geometry” appear here)
Olaf Hohm, Henning Samtleben: U-duality covariant gravity, J. High Energ. Phys. 2013 80 (2013) [arXiv:1307.0509, doi:10.1007/JHEP09(2013)080]
The original articles introducing the terminologu of “exceptional field theory”:
Olaf Hohm, Henning Samtleben: Exceptional Form of Supergravity, Phys. Rev. Lett. 111 231601 (2013) [arXiv:1308.1673, doi:10.1103/PhysRevLett.111.231601]
Olaf Hohm, Henning Samtleben: Exceptional Field Theory I: covariant Form of M-Theory and Type IIB, Phys. Rev. D 89 066016 (2014) [arXiv:1312.0614, doi:10.1103/PhysRevD.89.066016]
Olaf Hohm, Henning Samtleben: Exceptional Field Theory II: , Phys. Rev. D 89 066017 (2014) [arXiv:1312.4542, doi:10.1103/PhysRevD.89.066017]
Olaf Hohm, Henning Samtleben: Exceptional Field Theory III: , Phys. Rev. D 90 066002 (2014) [arXiv:1406.3348, doi:10.1103/PhysRevD.90.066002]
Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Henning Samtleben: exceptional field theory I. The potential J. High Energ. Phys. 2019 89 (2019) [arXiv:1811.04088, doi:10.1007/JHEP03(2019)089]
Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Henning Samtleben: exceptional field theory II. The complete dynamics, J. High Energ. Phys. 2021 107 (2021). [arXiv:2103.12118, doi:10.1007/JHEP05(2021)107]
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:
Alexander G. Tumanov, Peter West, and exceptional field theory (arXiv:1507.08912)
Guillaume Bossard, Axel Kleinschmidt, Jakob Palmkvist, Christopher Pope, Ergin Sezgin, Beyond , JHEP 05 (2017) 020 [doi:10.1007/JHEP05(2017)020, arXiv:1703.01305]
Guillaume Bossard, Axel Kleinschmidt, Ergin Sezgin: On supersymmetric exceptional field theory, J. High Energ. Phys. 2019 165 (2019) [arXiv:1907.02080, doi:10.1007/JHEP10(2019)165]
Guillaume Bossard, Axel Kleinschmidt, Ergin Sezgin, A master exceptional field theory (arXiv:2103.13411)
Discussion for E9:
Generalization to exceptional super-spacetimes:
On AdS4/CFT3 duality via exceptional field theory and super Chern-Simons theory:
See also:
On application to KK-reduction of D=10 supergravity and D=11 supergravity on squashed 7-spheres:
Last revised on September 20, 2024 at 13:54:34. See the history of this page for a list of all contributions to it.