Yang-Mills Instantons and Dyons on Group Manifolds

Abstract

We consider Euclidean SU(N) Yang-Mills theory on the space GxR, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang-Mills equations. For gauge fields invariant under the adjoint G-action these BPS equations reduce to first-order matrix equations, to which we give instanton solutions. In the case of G=SU(2)=S^3, our matrix equations are recast as Nahm equations, and a further algebraic reduction to the Toda chain equations is presented and solved for the SU(3) example. Finally, we change the metric on GxR to Minkowski and construct finite-energy dyon-type Yang-Mills solutions. The special case of G=SU(2)xSU(2) may be used in heterotic flux compactifications.

1+7 pages

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• Solutions to Yang-Mills equations on four-dimensional de Sitter space
• Finite-action solutions of Yang-Mills equations on de Sitter dS${}_4$ and anti-de Sitter AdS${}_4$ spaces
• Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
• Yang-Mills Equations of Motion for the Higgs Sector of SU(3)-Equivariant Quiver Gauge Theories
• Yang-Mills solutions on de Sitter space of any dimension
• Yang-Mills solutions on Minkowski space via non-compact coset spaces
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• Explicit Construction of Hermitian Yang-Mills Instantons on Coset Manifolds
• Perturbations to Generalized Kink-like Topological Defects in $AdS$