Projects per year
Abstract
We calculate the Spencer cohomology of the (1,0) Poincar\'e superalgebras in six dimensions: with and without Rsymmetry. As the cases of four and eleven dimensions taught us, we may read off from this calculation a Killing spinor equation which allows the determination of which geometries admit rigidly supersymmetric theories in this dimension. We prove that the resulting Killing spinors generate a Lie superalgebra and determine the geometries admitting the maximal number of such Killing spinors. They are divided in two branches. One branch consists of the lorentzian Lie groups with biinvariant metrics and, as a special case, it includes the lorentzian Lie groups with a selfdual Cartan threeform which define the maximally supersymmetric backgrounds of (1,0) Poincar\'e supergravity in six dimensions. The notion of Killing spinor on the other branch does not depend on the choice of a threeform but rather on a oneform valued in the Rsymmetry algebra. In this case, we obtain three different (up to local isometry) maximally supersymmetric backgrounds, which are distinguished by the causal type of the oneform.
Original language  English 

Pages (fromto)  1344 
Number of pages  37 
Journal  Journal of geometry and physics 
Volume  132 
Early online date  5 Jun 2018 
DOIs  
Publication status  Published  Oct 2018 
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Projects
 1 Finished

Particle Theory at the Higgs Centre
FigueroaO'Farrill, J., Lucietti, J. & Simon Soler, J.
1/10/14 → 30/09/18
Project: Research