Testing complete positivity

We study the modified dynamical evolution of the neutral kaon system under the condition of complete positivity. The accuracy of the data from planned future experiments is expected to be sufficiently precise to test such a hypothesis.Comment: 12 pages, latex, no figures, to appear in Mod. Phys. Lett.

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