Moduli spaces of contact instantons on Sasakian 5-manifolds with transverse Calabi-Yau structures and orbifold K3 surfaces

Abstract

We study anti-self-dual contact instantons on 5-dimensional Sasakian manifolds with transverse Calabi-Yau structures. In this case, the leaf space is a Calabi-Yau orbifold, and the moduli space of irreducible anti-self-dual contact instantons is a hyperkahler manifold. Using the singularity data of the leaf spaces, we prove that the transverse Levi-Civita connection gives an irreducible anti-self-dual contact instanton in the case when the leaf space is one of the 95 orbifold $K3$ surfaces classified by Reid. Moreover, we compute explicitly the complex dimension of the corresponding moduli spaces in all 95 cases.