Abstract:
It has been shown in the work of Chakrabarti, Sherry and Tchrakian that the chiral SO ±(4 p) Yang–Mills theory in the Euclidean 4 p (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.
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Received: 20 May 1996 / Accepted: 30 April 1997
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Spruck, J., Tchrakian, D. & Yang, Y. Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes . Comm Math Phys 188, 737–751 (1997). https://doi.org/10.1007/s002200050186
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DOI: https://doi.org/10.1007/s002200050186