Instantons on conical half-flat 6-manifolds

TL;DR

This paper develops a method to construct special 6-manifolds with SU(3)-structure from 5-manifolds with SU(2)-structure, and explores instanton solutions on these manifolds relevant to string theory compactifications.

Contribution

It introduces a general procedure to generate half-flat and nearly Kahler 6-manifolds from 5-manifolds with SU(2)-structure and analyzes instanton equations on these new geometries.

Findings

Constructed half-flat and nearly Kahler 6-manifolds from SU(2)-structure 5-manifolds.

Reduced instanton equations to matrix equations on these manifolds.

Presented explicit solutions and configurations of instantons.

Abstract

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kahler in the special case of sine-cones over Sasaki-Einstein 5-manifolds. Both half-flat and nearly Kahler 6-manifolds are prominent in flux compactifications of string theory. Subsequently, we investigate instanton equations for connections on vector bundles over these half-flat manifolds. A suitable ansatz for gauge fields on these 6-manifolds reduces the instanton equation to a set of matrix equations. We finally present some of its solutions and discuss the instanton configurations obtained this way.