Certain parallels between HYM and special Lagrangians are already known to Thomas and Yau. The Chern connection $\nabla_{H}$ is analogous to the Lagrangian submanifold $L$ (with $U(1)$ local systems), the HYM equation as a first order equation on $\nabla_{H}$ is analogous to the special Lagrangian condition on $L$, the second order Yang-Mills equation is analogous to the minimal surface equation on $L$, and the Yang-Mills energy minimization is analogous to the volume minimization. If the Lagrangian $L$ is represented as the graph of an exact 1-form, then the potential function defining $L$ could be viewed as analogous to the Hermitian metric $H$. Finding a mirror analogue resembling the $\mu$-stability was one of Thomas and Yau’s principal motivations.