Moduli space metrics for axially symmetric instantons

Abstract

Under an axial symmetry the Yang–Mills self-duality equations for an arbitrary gauge group reduce to the Toda equation for that particular group, from which the finite action instantons (hyperbolic vortices) may be constructed. The space of such finite action instantons, with gauge equivalent solutions identified, is known as the moduli space, and carries a naturally defined Kähler metric. This metric is studied for the simply laced Lie algebras, and explicit examples are constructed for the 2-vortex system.