Instantons and Yang-Mills Flows on Coset Spaces

Abstract

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to phi^4-kink equations on R. Depending on the boundary conditions and torsion, we obtain solutions to the Yang-Mills equations describing instantons, chains of instanton-anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang-Mills flow equations and compare them with the Yang-Mills solutions on R x G/H.

1+12 pages

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• Instantons on Special Holonomy Manifolds
• Solutions to Yang-Mills equations on four-dimensional de Sitter space
• Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
• Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
• 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
• Instantons on sine-cones over Sasakian manifolds
• Yang-Mills solutions on Minkowski space via non-compact coset spaces
• Yang-Mills solutions on de Sitter space of any dimension
• Homogeneous heterotic supergravity solutions with linear dilaton
• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
• Explicit Non-Abelian Gerbes with Connections
• Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
• Explicit Construction of Hermitian Yang-Mills Instantons on Coset Manifolds