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<p>It is known that hyperbolic monopoles, with a particular value of the curvature, can be obtained from ADHM instanton data that satisfies additional constraints. Here this data is reformulated in terms of a triplet of real matrices that satisfy a set of quartic equations, with solutions associated with representations of 𝔰𝔲(2). Many of the known examples of hyperbolic monopoles can easily be recovered in this formulation by evaluating Nahm data for Euclidean monopoles at the centre of its domain. Toda reductions of Nahm’s equation correspond to cyclic Euclidean monopoles, and this is adapted to the hyperbolic setting to obtain solutions, even when the corresponding Nahm data is not tractable. A new family of charge 4 hyperbolic monopoles with square symmetry is presented as an example.</p>

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Hyperbolic monopole data

  • 期刊论文

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  • 发表日期：

    2026年2月11日

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  • Paul Sutcliffe

摘要

It is known that hyperbolic monopoles, with a particular value of the curvature, can be obtained from ADHM instanton data that satisfies additional constraints. Here this data is reformulated in terms of a triplet of real matrices that satisfy a set of quartic equations, with solutions associated with representations of 𝔰𝔲(2). Many of the known examples of hyperbolic monopoles can easily be recovered in this formulation by evaluating Nahm data for Euclidean monopoles at the centre of its domain. Toda reductions of Nahm’s equation correspond to cyclic Euclidean monopoles, and this is adapted to the hyperbolic setting to obtain solutions, even when the corresponding Nahm data is not tractable. A new family of charge 4 hyperbolic monopoles with square symmetry is presented as an example.