Hermitian Yang-Mills instantons on Calabi-Yau cones

TL;DR

This paper constructs explicit non-abelian Hermitian Yang-Mills instantons on Calabi-Yau cones by reducing the equations to a Higgs-Yang-Mills flow and solving it explicitly, revealing new instanton solutions.

Contribution

It introduces a novel approach to find Hermitian Yang-Mills instantons on Calabi-Yau cones via a Higgs-Yang-Mills flow reduction and provides explicit solutions for any 2d-dimensional case.

Findings

Explicit solutions for non-abelian HYM instantons on Calabi-Yau cones.

Reduction of HYM equations to a Higgs-Yang-Mills flow on the Einstein-Kahler base.

Instantons as deformations of the spin connection.

Abstract

We study and construct non-abelian hermitian Yang-Mills (HYM) instantons on Calabi-Yau cones. By means of a particular isometry preserving ansatz, the HYM equations are reduced to a novel Higgs-Yang-Mills flow on the Einstein-Kahler base. For any 2d-dimensional Calabi-Yau cone, we find explicit solutions of the flow equations that correspond to non-trivial SU(d) HYM instantons. These can be regarded as deformations of the spin connection of the Calabi-Yau cone.