We construct explicit examples of deformed $G_2$-instantons on $\mathbb{R}^4 \times S^3$ endowed with the torsion free $G_2$-structure found by Brandhuber et al. These are the first such non-trivial examples on a $G_2$ manifold. We also construct examples on the Bryant-Salamon cone.
$SU(2)^2$-invariant $G_2$-instantons
New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$
Instantons and curves on class VII surfaces
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