Instantons and Killing spinors

TL;DR

This paper constructs and analyzes instantons on manifolds with Killing spinors and their cones, demonstrating solutions to the instanton and Yang-Mills equations, and applying these to heterotic supergravity, including new solutions.

Contribution

It introduces a method to construct instantons on manifolds with Killing spinors and their cones, linking instanton solutions to heterotic supergravity.

Findings

Constructed instantons on manifolds with Killing spinors.

Proved instanton equation implies Yang-Mills equation with torsion.

Produced new instanton solutions on Euclidean spaces.

Abstract

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. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.