Existence of Hyperbolic Calorons

Abstract

Recent work of Harland shows that the $SO(3)$-symmetric, dimensionally-reduced, charge-$N$ self-dual Yang--Mills calorons on the hyperbolic space $H^3\times S^1$ 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.

19 pages, accepted for publication, Proceedings of Royal Society (London), Series A, 2015

References in corpus (2)

• Hyperbolic calorons, monopoles, and instantons
• Singular instantons with SO(3) symmetry

Cited by in corpus (1)

• Nonlinear Problems Inspired by the Born--Infeld Theory of Electrodynamics