A hyperholomorphic line bundle on certain hyperkähler manifolds not admitting an S1-symmetry

Generalizing work of Haydys [7] and Hitchin [8], we prove the existence of a hyperholomorphic line bundle on certain hyperkähler manifolds that do not necessarily admit an S1 action. As examples, we consider the moduli space of (non-strongly) parabolic Higgs bundles, the moduli space of solutions to Nahm's equations, and Nakajima quiver varieties.