exceptional generalized geometry
A variant of the idea of generalized complex geometry given by passing from generalization of complex geometry to generalization of exceptional geometry. Instead of by reduction of structure groups along inclusions like it is controled by inclusions of into split real forms of exceptional Lie groups.
This serves to neatly encode U-duality groups in supergravity as well as higher supersymmetry of supergravity compactifications. See also at exceptional field theory, for more on this.
Compactification of 11-dimensional supergravity on a manifold of dimension 7 preserves supersymmetry precisely if its generalized tangent bundle has G-structure for the inclusion
of the special unitary group in dimension 7 into the split real form of E7. This is shown in (Pacheco-Waldram 08).
One dimension down, compactification of 10-dimensional type II supergravity on a 6-manifold preserves supersymmetry precisely if the generalized tangent bundle in the NS-NS sector admits G-structure for the inclusion
This is reviewed in (GLSW, section 2).
- David Baraglia, Leibniz algebroids, twistings and exceptional generalized geometry (arXiv:1101.0856)
Survey slides include
- David Baraglia, Exceptional generalized geometry and backgrounds (pdf)
Daniel Persson, Arithmetic and Hyperbolic Structures in String Theory (arXiv:1001.3154)
Nassiba Tabti, Kac-Moody algebraic structures in supergravity theories (arXiv:0910.1444)
Original articles include
K. Koepsell, Hermann Nicolai, Henning Samtleben, An exceptional geometry for d=11 supergravity?, Class.Quant.Grav.17:3689-3702,2000 (arXiv:hep-th/0006034)
Chris Hull, Generalised Geometry for M-Theory, JHEP 0707:079 (2007) (arXiv:hep-th/0701203)
Paulo Pires Pacheco, Daniel Waldram, M-theory, exceptional generalised geometry and superpotentials, JHEP 0809:123,2008 (arXiv:0804.1362)
Mariana Graña, Jan Louis, Aaron Sim, Daniel Waldram, formulation of backgrounds (arXiv:0904.2333)
G. Aldazabala, E. Andrésb, P. Cámarac, Mariana Graña, U-dual fluxes and generalized geometry, JHEP 1011:083,2010 (arXiv:1007.5509)
Mariana Graña, Francesco Orsi, vacua in Exceptional Generalized Geometry (arXiv:1105.4855)
E6,E7, E8-geometry is discussed in
(see also at 3d supergravity – possible gaugings).
The E10-geometry of 11-dimensional supergravity compactified to the line is discussed in
The E11-geometry of 11-dimensional supergravity compactified to the point is discussed in
The generalized-U-duality+diffeomorphsim invariance in 11d is discussed in
For the worldvolume theory of the M5-brane this is discussed in
- Machiko Hatsuda, Kiyoshi Kamimura, M5 algebra and duality (arXiv:1305.2258)
Relation to Borcherds superalgebras is surveyed and discussed in
- Jakob Palmkvist, Exceptional geometry and Borcherds superalgebras (arXiv:1507.08828)
Revised on August 19, 2015 19:09:06
by Urs Schreiber