Sasakian Geometry, Holonomy, and Supersymmetry
Charles P. Boyer, Krzysztof Galicki
TL;DR
This paper explores the connections between Sasakian geometry, holonomy, and supersymmetry, highlighting how special geometric structures relate to physical theories and their mathematical properties.
Contribution
It provides an expository overview of the relationships between Sasakian geometry, reduced holonomy, and supersymmetry, emphasizing the geometric structures admitting Killing spinors.
Findings
Sasaki-Einstein manifolds admit real Killing spinors.
7-manifolds with nearly parallel G2 structures relate to supersymmetry.
Nearly Kähler 6-manifolds are connected to Sasaki-Einstein geometry.
Abstract
In this expository article we discuss the relations between Sasakian geometry, reduced holonomy and supersymmetry. It is well known that the Riemannian manifolds other than the round spheres that admit real Killing spinors are precisely Sasaki-Einstein manifolds, 7-manifolds with a nearly parallel G2 structure, and nearly Kaehler 6-manifolds. We then discuss the relations between the latter two and Sasaki-Einstein geometry.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics