Yang-Mills flows on nearly Kaehler manifolds and G_2-instantons

Abstract

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, RxG/H and R^2xG/H, where G/H is a compact nearly Kaehler six-dimensional homogeneous space, and the manifolds RxG/H and R^2xG/H carry G_2- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on RxG/H is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G_2-structures on RxG/H. It is shown that both G_2-instanton equations can be obtained from a single Spin(7)-instanton equation on R^2xG/H.

1+21 pages, 3 figures v2: clarifying comments and references added, published version

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Cited by in corpus (36)

• Instantons and Killing spinors
• Yang-Mills instantons and dyons on homogeneous G_2-manifolds
• The infinitesimal moduli space of heterotic $G_2$ systems
• Double quiver gauge theory and nearly Kahler flux compactifications
• Instantons on Special Holonomy Manifolds
• Flag manifold sigma models: spin chains and integrable theories
• Instantons on the exceptional holonomy manifolds of Bryant and Salamon
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Moduli Spaces of Contact Instantons
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
• Deformations of nearly Kähler instantons
• SU(2) solutions to self-duality equations in eight dimensions
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Generalised Chern-Simons Theory and ${\mathrm{G}}_2$-Instantons over Associative Fibrations
• Geometry and Energy of Non-abelian Vortices
• Marginal deformations of heterotic $G_2$ sigma models
• Instantons on sine-cones over Sasakian manifolds
• Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structure
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• Left-invariant Einstein metrics on $S^3\times S^3$
• Instantons on Calabi-Yau cones
• Instantons on the six-sphere and twistors
• Homogeneous heterotic supergravity solutions with linear dilaton
• Instantons on conical half-flat 6-manifolds
• (1,0) gauge theories on the six-sphere
• A Twistor Space Action for Yang-Mills Theory
• Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories
• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
• Instantons and Chern-Simons flows in 6, 7 and 8 dimensions
• Deformation Theory of Asymptotically Conical Spin(7)-Instantons
• Skyrme-Faddeev model from 5d super-Yang-Mills
• Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
• Instantons on Calabi-Yau and hyper-Kähler cones
• Gravity and induced matter on Nearly Kahler Manifolds
• Explicit Construction of Hermitian Yang-Mills Instantons on Coset Manifolds