Existence of hyperbolic calorons.

Recent work of Harland shows that the SO(3)-symmetric, dimensionally reduced, charge-N self-dual Yang-Mills calorons on the hyperbolic space [Formula: see text] may be obtained through constructing N-vortex solutions of an Abelian Higgs model as in the study of Witten on multiple instantons. In this paper, we establish the existence of such minimal action charge-N calorons by constructing arbitrarily prescribed N-vortex solutions of the Witten type equations.