### Abstract

We revisit the problem of constructing instantons on ADE orbifolds R-4/Gamma and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R-4/Gamma which are BPS equations for the Yang-Mills equations with an external current. The relation between level sets of the moment maps in the hyper-Kahler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically symmetric Gamma-equivariant connections on complex V bundles over R-4/Gamma which are tailored to the way in which the orbifold group acts on the fibers. Some explicit Abelian and non-Abelian SU(2)-invariant solutions to the instanton equations on the orbifold are worked out.

Original language | English |
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Article number | 105026 |

Number of pages | 10 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 88 |

Issue number | 10 |

DOIs | |

Publication status | Published - Nov 2013 |

### Keywords

- GRAVITATIONAL INSTANTONS
- ALE SPACES
- HYPERKAHLER METRICS
- FIELD-THEORY
- GEOMETRY
- CONSTRUCTION
- VARIETIES

## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*88*(10), [105026]. https://doi.org/10.1103/PhysRevD.88.105026