Multiple instantons representing higher-order Chern-Pontryagin classes

Joel Spruck, D. H. Tchrakian, Yisong Yang

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - 1997

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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