Multiple instantons representing higher-order Chern-Pontryagin classes

Joel Spruck, D. H. Tchrakian, Yisong Yang

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)737-751
Number of pages15
JournalCommunications in Mathematical Physics
Volume188
Issue number3
StatePublished - 1997

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Instantons
instantons
Higher Order
Charge
existence theorems
uniqueness theorem
half planes
Variational Equation
Existence and Uniqueness Theorem
Yang-Mills
Yang-Mills Theory
Yang-Mills theory
Half-plane
Higher Dimensions
System of equations
Class
Euclidean
Nonlinear Equations
High-dimensional
Unit

ASJC Scopus subject areas

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

Cite this

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

In: Communications in Mathematical Physics, Vol. 188, No. 3, 1997, p. 737-751.

Research output: Contribution to journalArticle

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