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

^(a) vlslesar@central.ucv.ro
^(b) mvisin@theory.nipne.ro
^(c) gvilcu@upg-ploiesti.ro
gvilcu@gta.math.unibuc.ro

Received: 17 March 2015
Accepted: 20 April 2015

Abstract

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 T^1,1.