### 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) |
---|---|

Pages (from-to) | 737-751 |

Number of pages | 15 |

Journal | Communications in Mathematical Physics |

Volume | 188 |

Issue number | 3 |

State | Published - 1997 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*188*(3), 737-751.

**Multiple instantons representing higher-order Chern-Pontryagin classes.** / Spruck, Joel; Tchrakian, D. H.; Yang, Yisong.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 188, no. 3, pp. 737-751.

}

TY - JOUR

T1 - Multiple instantons representing higher-order Chern-Pontryagin classes

AU - Spruck, Joel

AU - Tchrakian, D. H.

AU - Yang, Yisong

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031256162&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031256162&partnerID=8YFLogxK

M3 - Article

VL - 188

SP - 737

EP - 751

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -