Volume 110, Number 3, May 2015
|Number of page(s)||6|
|Section||The Physics of Elementary Particles and Fields|
|Published online||15 May 2015|
Hidden symmetries on toric Sasaki-Einstein spaces
1 Department of Mathematics, University of Craiova - Str. Al.I. Cuza, Nr. 13, Craiova 200585, Romania
2 Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering Magurele, P.O. Box M.G.-6, Romania
3 Department of Cybernetics and Economic Informatics, Petroleum-Gas University of Ploieşti Bd. Bucureşti, Nr. 39, Ploieşti 100680, Romania
4 Faculty of Mathematics and Computer Science, Research Center in Geometry, Topology and Algebra, University of Bucharest - Str. Academiei, Nr. 14, Sector 1, Bucharest 060042, Romania
Received: 17 March 2015
Accepted: 20 April 2015
We describe the construction of Killing-Yano tensors on toric Sasaki-Einstein manifolds. We use the fact that the metric cones of these spaces are Calabi-Yau manifolds. The description of the Calabi-Yau manifolds in terms of toric data, using the Delzant approach to toric geometries, allows us to find explicitly the complex coordinates and write down the Killing-Yano tensors. As a concrete example we present the complete set of special Killing forms on the five-dimensional homogeneous Sasaki-Einstein manifold T1,1.
PACS: 11.30.-j – Symmetry and conservation laws / 11.30.Ly – Other internal and higher symmetries / 02.40.Tt – Complex manifolds
© EPLA, 2015
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