Killing spinors, from general relativity to supergravity
Seminar Room 2, Newton Institute Gatehouse
Killing spinors first appeared in an article by R. Penrose and M. Walker devoted to the search of quadratic first integrals of the geodesic flow on special space-times, i.e. in the context of General Relativity.
Later Killing spinors were recognized as the counterpart in supergeometry of Killing fields. This gave rise to an extensive study of the overdetermined system that defines them. A classification in the Riemannian case has been obtained, and their role in the limiting case for the lowest eigenvalue of the Dirac operator on compact manifolds.
Since Killing spinors are linked in some way to holonomy questions, it is not surprising to realize that the situation concerning them in Lorentzian and in Riemannian geometries are rather different.
Several generalisations of Killing spinors have been considered recently in relation to Supergravity models involving an exterior differential 3-form, with special attention devoted to the 7- and 11-dimensional cases.