Consider a holomorphic line bundle L over a compact Kahler manifold. Motivated by mirror symmetry, I will define an equation on L that is the line bundle analogue of the special Lagrangian equation, which can be studied even when the base is not a Calabi-Yau manifold. I will show solutions are unique global minimizers of a positive functional. To address existence, I will introduce a line bundle analogue of the Lagrangian mean curvature flow, and prove convergence in certain cases. This is joint work with S.-T. Yau.