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 N\"olle [D. Harland and C. N\"olle, J. High Energy Phys. 03 (2012) 082.] in such a way that instantons are parametrized by constrained matrix-valued functions. Our ansatz reduces instanton equations to matrix model equations which can be further reduced to Newtonian mechanics with particle trajectories obeying first-order gradient flow equations. Generalizations to K\"ahler-Einstein manifolds and resolved Calabi-Yau cones are briefly discussed. Our construction allows one to associate quiver gauge theories with special holonomy manifolds via dimensional reduction.