We describe moreover a natural Yang–Mills theory on such spaces, with many important features of the torsion-free case, such as a Chern–Simons formalism and topological energy bounds. In fact, compatible $\mathrm G_2$-instantons on holomorphic Sasakian bundles over $K$ are exactly the transversely Hermitian Yang–Mills connections. As a proof of principle, we obtain $\mathrm G_2$-instantons over the Fermat quintic link from stable bundles over the smooth projective Fermat quintic, thus relating in a concrete example the Donaldson–Thomas theory of the quintic threefold with a conjectural $\mathrm G_2$-instanton count.

我们还描述了关于此类空间的自然Yang-Mills理论，具有无扭转情况的许多重要特征，例如Chern-Simons形式主义和拓扑能界。实际上，在$ K $以上的全纯Sasakian束上兼容的$ \ mathrm G_2 $ -instantons正好是横向Hermitian Yang-Mills连接。作为原理上的证明，我们从平稳射影的Fermat五次方程组的稳定束中，通过Fermat五次函数链接获得$ \ mathrm G_2 $ -instantons，因此在一个具体示例中将五次方程的唐纳森-托马斯理论与一个猜想$ \ mathrm G_2 $ -instanton计数。