Symmetric Instantons and Discrete Hitchin Equations

TL;DR

This paper explores how symmetric instantons in gauge theory relate to integrable lattice systems, revealing a new discrete version of the Hitchin equations derived from generalized ADHM data.

Contribution

It introduces a novel two-dimensional lattice system arising from $T^2$-symmetric instantons, extending the connection between instantons and integrable systems.

Findings

$T^2$-symmetric instantons lead to a 2D integrable lattice system.

This system serves as a discrete analogue of the Hitchin equations.

The work generalizes the known $S^1$-symmetric case to a $T^2$-symmetric setting.

Abstract

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.