Euclidean supersymmetric solutions with the selfdual Weyl tensor
Abstract
We explore the Euclidean supersymmetric solutions admitting the selfdual gauge field in the framework of N = 2 minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the PrzanowskiTod class with the selfdual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the PrzanowskiTod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another PrzanowskiTod form. This formalism enables us to show that the selfdual ReissnerNordströmTaubNUTAdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the PrzanowskiTod space is conformal to each of the selfdual ambitoric Kähler metrics. It turns out that three classes of solutions are all reduced to the selfdual Carter family, by virtue of the nondegenerate KillingYano tensor.
 Publication:

Physics Letters B
 Pub Date:
 July 2017
 DOI:
 10.1016/j.physletb.2017.04.064
 arXiv:
 arXiv:1702.05210
 Bibcode:
 2017PhLB..770..166N
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 v2: 10 pages, refs. added, typos corrected, version to appear in PLB