Bernd Ammann, University of Regensburg
Parallel spinors, i.e. parallel sections of the spinor bundle, are related to many problems in mathematics and physics. All known compact Ricci-flat Riemannian manifolds have a finite covering that admits a parallel spinor. In physics they seem to be related to supersymmetry and hidden dimensions. Parallel spinors lead to special holonomy.
In the talk we will present unexpected tight relations between Lorentzian metrics of dimension n + 1 carrying a parallel (lightlike) spinor and 1-parameter families of Riemannian metrics carrying a parallel spinors on an (n−1)-dimensional manifold.
The subject is connected to metrics with special holonomy, more precisely to manifolds with restricted holonomy SU (k) (Calabi-Yau), Sp(k) (hyper-Kähler), G2, Spin(7) and products thereof. Curves in the associated moduli spaces of Riemannian metrics give rise to Lorentzian manifolds with a parallel spinor and vice versa.
The talk will report about previous work by Baum, Leistner and Lischewski (2014–2017) and on current work with Klaus Kröncke, Olaf Müller and Jonathan Glöckle, partially work in progress.