Holomorphic lagrangian branes correspond to perverse sheaves

Let X be a compact complex manifold, D^b_c(X) be the bounded derived category of constructible sheaves on X, and Fuk(T*X) be the Fukaya category of T*X . A Lagrangian brane in Fuk(T*X) is holomorphic if the underlying Lagrangian submanifold is complex analytic in T*X_C, the holomorphic cotangent bundle of X . We prove that under the quasiequivalence between D^b_c(X) and DFuk(T *X) established by Nadler and Zaslow, holomorphic Lagrangian branes with appropriate grading correspond to perverse sheaves.