Instantons on Special Holonomy Manifolds

Understand

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.