The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.
We derive an exact equation for simple self non-intersecting Wilson loops in non-Abelian gauge theories with gauge fields interacting with fermions in two-dimensional Euclidean space.
Exact Classical Solutions of the Coupled System of O(5) Gauge Fields with Massless Scalar Fields in Euclidean Space