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We give a construction of $G_2$ and $Spin(7)$ instantons on exceptionalholonomy manifolds constructed by Bryant and Salamon, by using an ansatz ofspherical symmetry coming from the manifolds being the total spaces of rank-4vector bundles. In the $G_2$ case, we show that, in the asymptotically conicalmodel, the connections are asymptotic to Hermitian Yang-Mills connections onthe nearly K\"ahler $S^3\times S^3$.

Instantons on the exceptional holonomy manifolds of Bryant and Salamon