Special Lagrangian cycles and Hermitian Yang-Mills connections

We consider the adiabatic limit of a sequence of Hermitian Yang-Mills connections on a SU(r)-bundle over a semi-flat smooth special Lagrangian torus fibration pi : M --> B. The restriction of these connections to the fiber tori can be viewed as a family of SU(r)-connections on the fiber tori which are parameterized by B. We show that there is a gauge equivalent subsequence such that the restriction of each connection to the fiber tori converges in the Hausdorff topology, away from some closed subset of B of codimension at least two, to a limit which defines a r-sheeted special Lagrangian cycle in the dual special Lagrangian torus fibration.