Generalized Cartan Calculus in general dimension
Abstract
We develop the generalized Cartan Calculus for the groups and SO(5 , 5). They are the underlying algebraic structures of d = 9 , 7 , 6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincaré lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- July 2015
- DOI:
- arXiv:
- arXiv:1504.04780
- Bibcode:
- 2015JHEP...07..114W
- Keywords:
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- Differential and Algebraic Geometry;
- String Duality;
- Space-Time Symmetries;
- Supergravity Models;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- 30 pages