Sasakian geometry, holonomy, and supersymmetry

Abstract

The main purpose of this review is to describe geometric properties of Sasaki–Einstein manifolds which make them interesting in modern theoretical physics. In spite of the fact that it is supersymmetry that connects Sasaki–Einstein spaces to physics, it is not the purpose of this article to describe what this concept really means to either physicists or mathematicians. There have been many recent attempts to frame these important notions of theoretical physics in precise mathematical terms. This enormous task is far beyond the scope of this article. Here we content ourselves with providing the main theorems and results concerning Killing spinors.