Examples of deformed Spin(7)-instantons/Donaldson-Thomas connections

Abstract: We construct examples of deformed Hermitian Yang-Mills connections and deformed Spin(7)-instantons (also called Spin(7) deformed Donaldson-Thomas connections) on the cotangent bundle of $\mathbb{C}\mathbb{P}^2$ endowed with the Calabi hyperK\"ahler structure. Deformed Spin(7)-instantons on cones over 3-Sasakian 7-manifolds are also constructed. We show that these can be used to distinguish between isometric structures and also between Sp(2) and Spin(7) holonomy cones. To the best of our knowledge, these are the first non-trivial examples of deformed Spin(7)-instantons.