Examples of deformed G_2-instantons/Donaldson-Thomas connections

TL;DR

This paper presents the first non-trivial examples of deformed G_2-instantons, illustrating their role in distinguishing G_2-structures and analyzing their moduli spaces, with implications for geometric analysis and gauge theory.

Contribution

It provides explicit examples of deformed G_2-instantons with obstructed deformation theory and explores their relation to a Chern-Simons type functional.

Findings

Examples distinguish nearly parallel and isometric G_2-structures.

Moduli space components have different dimensions.

Deformed G_2-instantons are critical points of a Chern-Simons type functional.

Abstract

In this note, we provide the first non-trivial examples of deformed G_2-instantons, originally called deformed Donaldson-Thomas connections. As a consequence, we see how deformed G_2-instantons can be used to distinguish between nearly parallel G_2-structures and isometric G_2-structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed G_2-instantons with obstructed deformation theory and situations where the moduli space of deformed G_2-instantons has components of different dimensions. We finally study the relation between our examples and a Chern-Simons type functional which has deformed G_2-instantons as critical points.