Complex anti-self dual connections on a product of Calabi-Yau surfaces and triholomorphic curves

We study the adiabatic limit of a sequence of Omega-anti-self-dual connections on unitary bundles over a product of two compact Calabi-Yau surfaces M x N by scaling metrics to shrink N to a point. We show that after fixing gauge transformations, a subsequence of the N-components of these connections converges to a triholomorphic curve from M away from a Cayley cycle in M x N to the moduli space M-N of instantons on N module gauge equivalence in the Hausdorff topology, and converges on the blowup locus to a family, which is parameterized by the Cayley cycle, of triholomorphic curves from C-2 to M-N.