Symmetric Instantons and Discrete Hitchin Equations

2015/09/30 by R. S. Ward, Ward, R. S.
Physics and Astronomy · #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.1509.09128

openalex publication_date 2015/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Self-dual Yang-Mills instantons on R⁴ correspond to algebraic ADHM data. The ADHM equations for S¹-symmetric instantons give a one-dimensional integrable lattice system, which may be viewed as an discretization of the Nahm equations. In this note, we see that generalized ADHM data for T²-symmetric instantons gives an integrable two-dimensional lattice system, which may be viewed as a discrete version of the Hitchin equations.

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