Yang-Mills instantons and dyons on homogeneous G_2-manifolds

Abstract

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of a particle moving in R^6, R^4 or R^2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)xU(1), Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink- and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S^1 x G/H and dyons on iR x G/H are also given.

1+26 pages, 14 figures, 6 miniplots

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Cited by in corpus (21)

• The infinitesimal moduli space of heterotic $G_2$ systems
• Double quiver gauge theory and nearly Kahler flux compactifications
• Notes on Yang-Mills--Higgs monopoles and dyons on R^D, and Chern-Simons--Higgs solitons on \R^{D-2}: Dimensional reduction of Chern-Pontryagin densities
• Instantons on Special Holonomy Manifolds
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Solutions to Yang-Mills equations on four-dimensional de Sitter space
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• 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
• Instantons on sine-cones over Sasakian manifolds
• Yang-Mills solutions on de Sitter space of any dimension
• Sasakian quiver gauge theories and instantons on the conifold
• Instantons on Calabi-Yau cones
• Sasakian quiver gauge theory on the Aloff-Wallach space $X_{1,1}$
• Instantons, five-branes and fractional strings
• Cho decomposition, Abelian gauge fixing and monopoles in G(2) Yang-Mills theory
• Instantons and Chern-Simons flows in 6, 7 and 8 dimensions
• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
• Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
• Instantons on Calabi-Yau and hyper-Kähler cones
• Instantons on Cylindrical Manifolds