Positive mass theorem in extended supergravities

Following the Witten-Nester formalism, we present a useful prescription using Weyl spinors towards the positivity of mass. As a generalization of arXiv:1310.1663, we show that some "positivity conditions" must be imposed upon the gauge connections appearing in the supercovariant derivative acting on spinors. A complete classification of the connection fulfilling the positivity conditions is given. It turns out that these positivity conditions are indeed satisfied for a number of extended supergravity theories. It is shown that the positivity property holds for the Einstein-complex scalar system, provided that the target space is Hodge-Kahler and the potential is expressed in terms of the superpotential. In the Einstein-Maxwell-dilaton theory with a dilaton potential, the dilaton coupling function and the superpotential are fixed by the positive mass property. We also explore the $N=8$ gauged supergravity and demonstrate that the positivity of the mass holds independently of the gaugings and the deformation parameters.Comment: v2: 22 pages, typos fixed and refs added, a section discussing the Einstein-Maxwell-dilaton theory added, an appendix classifies the connection satisfying positivity conditions, accepted for publication in NP

Black holes in an expanding universe and supersymmetry

This paper analyzes the supersymmetric solutions to five and six-dimensional minimal (un)gauged supergravities for which the bilinear Killing vector constructed from the Killing spinor is null. We focus on the spacetimes which admit an additional ${\rm SO}(1,1)$ boost symmetry. Upon the toroidal dimensional reduction along the Killing vector corresponding to the boost, we show that the solution in the ungauged case describes a charged, nonextremal black hole in a Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe with an expansion driven by a massless scalar field. For the gauged case, the solution corresponds to a charged, nonextremal black hole embedded conformally into a Kantowski-Sachs universe. It turns out that these dimensional reductions break supersymmetry since the bilinear Killing vector and the Killing vector corresponding to the boost fail to commute. This represents a new mechanism of supersymmetry breaking that has not been considered in the literature before.Comment: 9 pages, 1 figure; v2: minor modifications, published version in PL

Geometry of Killing spinors in neutral signature

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 $\Lambda<0$ non-null case, the canonical form of the metric is described by a fibration over a three-dimensional base space that has $\text{U}(1)$ 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-K\"ahler manifold, and admitting in addition a charged conformal Killing spinor. In the $\Lambda<0$ null case, the supersymmetric solutions define an integrable null K\"ahler structure. In the $\Lambda>0$ non-null case, the manifold is a fibration over a Lorentzian Gauduchon-Tod base space. Finally, in the $\Lambda>0$ null class, the metric is contained in the Kundt family, and it turns out that the holonomy is reduced to ${\rm Sim}(1)\times{\rm Sim}(1)$. There appear no self-dual solutions in the null class for either sign of the cosmological constant.Comment: 40 pages, uses JHEP3.cls. v2: Appendix and ref. added. v3: Published versio