Examples of deformed G2-instantons/Donaldson–Thomas connections

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.