On the Solutions of Generalized Bogomolny Equations

Abstract

Generalized Bogomolny equations are encountered in the localization of the topological N=4 SYM theory. The boundary conditions for 't Hooft and surface operators are formulated by giving a model solution with some special singularity. In this note we consider the generalized Bogomolny equations on a half space and construct model solutions for the boundary 't Hooft and surface operators. It is shown that for the 't Hooft operator the equations reduce to the open Toda chain for arbitrary simple gauge group. For the surface operators the solutions of interest are rational solutions of a periodic non-abelian Toda system.