Instantons and Killing spinors

Understand

We investigate instantons on manifolds with Killing spinors and their cones.

• Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds.
• We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion.
• We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity.