Associated with every quaternionic representation of a compact, connected Lie group there is a Seiberg–Witten equation in dimension three. The moduli spaces of solutions to these equations are typically non-compact. We construct Kuranishi models around boundary points of a partially compactified moduli space. The Haydys correspondence identifies such boundary points with Fueter sections—solutions of a non-linear Dirac equation—of the bundle of hyperkähler quotients associated with the quaternionic representation. We discuss when such a Fueter section can be deformed to a solution of the Seiberg–Witten equation.

中文翻译：

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三维三维爆炸Seiberg-Witten方程的变形理论

与紧密连接的李群的每个四元数表示相关，在三维中存在一个Seiberg-Witten方程。这些方程的解的模空间通常是非紧致的。我们围绕部分压缩模空间的边界点构造Kuranishi模型。Haydys对应关系使用与四元离子表示法相关的一堆超khähler商的Fueter截面（非线性Dirac方程的解）来标识此类边界点。我们讨论了何时可以将这样的Fueter截面变形为Seiberg-Witten方程的解。