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.
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).
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
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)
Revised on May 24, 2014 01:23:01
by Urs Schreiber