Killing superalgebras for lorentzian six-manifolds
| Autor: | Paul de Medeiros, José Figueroa-O’Farrill, Andrea Santi |
|---|---|
| Přispěvatelé: | de Medeiros, Paul, Figueroa-O’Farrill, José, Santi, Andrea |
| Rok vydání: | 2018 |
| Předmět: |
High Energy Physics - Theory
Mathematics - Differential Geometry 010308 nuclear & particles physics FOS: Physical sciences General Physics and Astronomy Killing superalgebras Rigid supersymmetry Spencer cohomology 01 natural sciences General Relativity and Quantum Cosmology High Energy Physics - Theory (hep-th) Differential Geometry (math.DG) 0103 physical sciences FOS: Mathematics Mathematics::Differential Geometry Geometry and Topology Representation Theory (math.RT) Mathematics - Representation Theory Mathematical Physics |
| Zdroj: | de Medeiros, P, Figueroa-O'Farrill, J & Santi, A 2018, ' Killing superalgebras for Lorentzian six-manifolds ', Journal of geometry and physics, vol. 132, pp. 13-44 . https://doi.org/10.1016/j.geomphys.2018.05.019 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2018.05.019 |
| Popis: | We calculate the Spencer cohomology of the $(1,0)$ Poincar\'e superalgebras in six dimensions: with and without R-symmetry. 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 bi-invariant metrics and, as a special case, it includes the lorentzian Lie groups with a self-dual Cartan three-form 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 three-form but rather on a one-form valued in the R-symmetry algebra. In this case, we obtain three different (up to local isometry) maximally supersymmetric backgrounds, which are distinguished by the causal type of the one-form. Comment: 38 pages (final version to appear in Journal of Geometry and Physics) |
| Databáze: | OpenAIRE |
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