Instantons on Special Holonomy Manifolds

Abstract

We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a connection proposed by Harland and Nolle in such a way that instantons are parameterized by constrained matrix-valued functions. Our ansatz reduces instanton equations to a matrix model equations which can be further reduced to Newtonian mechanics with particle trajectories obeying first-order gradient flow equations. Generalizations to Kaehler-Einstein manifolds and resolved Calabi-Yau cones are briefly discussed. Our construction allows one to associate quiver gauge theories with special holonomy manifolds.

20 pages; v2: clarifying comments added, published version

References in corpus (9)

• Integrability of Vortex Equations on Riemann Surfaces
• Non-Abelian Vortices on Riemann Surfaces: an Integrable Case
• Quiver Gauge Theory and Noncommutative Vortices
• SU(3)-Equivariant Quiver Gauge Theories and Nonabelian Vortices
• Instantons and Yang-Mills Flows on Coset Spaces
• Sasakian Geometry, Holonomy, and Supersymmetry
• Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
• Construction of Noncommutative Instantons in 4k Dimensions
• Hermitian Yang-Mills instantons on resolutions of Calabi-Yau cones

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• Generalised Chern-Simons Theory and ${\mathrm{G}}_2$-Instantons over Associative Fibrations
• Instantons on sine-cones over Sasakian manifolds
• Sasakian quiver gauge theories and instantons on cones over lens 5-spaces
• Instantons on Calabi-Yau cones
• Sasakian quiver gauge theories and instantons on the conifold
• Instantons on the six-sphere and twistors
• Instantons in six dimensions and twistors
• Sasakian quiver gauge theory on the Aloff-Wallach space $X_{1,1}$
• Instantons, five-branes and fractional strings
• Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
• Asymptotic behaviour of instantons on Cylinder Manifolds
• Instantons on Cylindrical Manifolds
• $L^2$ harmonic forms on complete special holonomy manifolds