Geometry of Killing spinors in neutral signature. (2nd September 2015)

• Record Type: Journal Article
• Authors: Klemm, Dietmar; Nozawa, Masato
• Is Part Of: Classical and quantum gravity. Volume 32:Number 18(2015:Sep.)
• Publication Date: 2015-09-02
• Subjects: superstring vacua -- classical theories of gravity -- supergravity models -- differential and algebraic geometry; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/32/18/185012
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: We classify the supersymmetric solutions of minimal N = 2 gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a bilinear of the Killing spinor is null or non-null. In neutral signature the bilinear vector field can be spacelike, which is a new feature not arising in Lorentzian signature. In the non-null case, the canonical form of the metric is described by a fibration over a three-dimensional base space that has holonomy with torsion. We find that a generalized monopole equation determines the twist of the bilinear Killing field, which is reminiscent of an Einstein–Weyl structure. If, moreover, the electromagnetic field strength is self-dual, one gets the Kleinian signature analogue of the Przanowski–Tod class of metrics, namely a pseudo-hermitian spacetime determined by solutions of the continuous Toda equation, conformal to a scalar-flat pseudo-Kähler manifold, and admitting in addition a charged conformal Killing spinor. In the null case, the supersymmetric solutions define an integrable null Kähler structure. In the non-null case, the manifold is a fibration over a Lorentzian Gauduchon–Tod base space. Finally, in the null class, the metric is contained in the Kundt family, and it turns out that the holonomy is reduced to . There appear no self-dual solutions in the null class for either sign of the cosmological constant.