Instantons on Special Holonomy Manifolds

Details Instantons on Special Holonomy Manifolds Instantons on Special Holonomy Manifolds

2012-03-12

arxiv.org/abs/1203.2657v2

Physics

High Energy Physics

High Energy Physics - Theory

20 pages; v2: clarifying comments added, published version

Scientific paper

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.

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