### Abstract

It has been shown in the work of Chakrabarti, Sherry and Tchrakian that the chiral SO_{±}(4p) Yang-Mills theory in the Euclidean 4p (p ≥ 2) dimensions allows an axially symmetric self-dual system of equations similar to Witten's instanton equations in the classical 4-dimensional SU(2) ∼ SO_{±}(4) theory and the solutions represent a new class of instantons. However the rigorous existence of these higher-dimensional instanton solutions has remained open except for the solution of unit charge representing a single instanton. In this paper we establish an existence and uniqueness theorem for multi-instantons of arbitrary charges in the case p ≥ 2. These solutions are the first known instantons, with the Chern-Pontryagin index greater than one, of the Yang-Mills model in higher dimensions. Our approach is a study of a nonlinear variational equation defined on the Poincaré half plane.

Original language | English (US) |
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Pages (from-to) | 737-751 |

Number of pages | 15 |

Journal | Communications In Mathematical Physics |

Volume | 188 |

Issue number | 3 |

DOIs | |

State | Published - 1997 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications In Mathematical Physics*,

*188*(3), 737-751. https://doi.org/10.1007/s002200050186