BIRS Workshop Lecture Videos
Supersymmetric backgrounds and generalised special holonomy Strickland-Constable, Charles
It is well known that, in the absence of internal fluxes, supersymmetric Minkowski backgrounds are given by manifolds with special Riemannian holonomy, such as the celebrated Calabi-Yau spaces. I will present recent work showing that general supersymmetric Minkowski flux backgrounds are precisely the analogues of these in generalised geometry. The generalised holonomy group is simply the natural stabiliser group of the Killing spinors, and depends only on the dimension and the number of preserved supersymmetries. The Killing superalgebra, which has a neat manifestation in this language, plays a key role in the proof of the main result for N > 2 supersymmetry and we are able to fix its form explicitly using this technology.
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