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Symmetric Instantons and Discrete Hitchin Equations

Self-dual Yang-Mills instantons on $R^4$ correspond to algebraic ADHM data. The ADHM equations for $S^1$-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 $T^2$-symmetric instantons gives an integrable two-dimensional lattice system, which may be viewed as a discrete version of the Hitchin equations.