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

TL;DR

This paper investigates the moduli spaces of anti-self-dual contact instantons on 5D Sasakian manifolds with transverse Calabi-Yau structures, revealing their hyperkähler nature and explicit dimensions for orbifold K3 cases.

Contribution

It establishes the hyperkähler structure of moduli spaces and explicitly computes their dimensions for all 95 orbifold K3 surface cases.

Findings

Moduli spaces are hyperkähler manifolds.

Transverse Levi-Civita connection yields irreducible anti-self-dual instantons.

Explicit dimension formulas for all 95 orbifold K3 cases.

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.