DHYM connections on higher rank holomorphic vector bundles over \({\mathbb {P}}(T_{{\mathbb {P}^{2}}})\)

We construct the first explicit non-trivial example of deformed Hermitian Yang–Mills (dHYM) connection on a higher rank slope-unstable holomorphic vector bundle over a Fano threefold. Additionally, we provide a sufficient algebraic condition in terms of central charges for the existence of dHYM connections on Whitney sum of holomorphic line bundles over rational homogeneous varieties. As a consequence, we obtain several new examples of dHYM connections on higher rank holomorphic vector bundles.