We construct exact t Hooft-Polyakov monopole solutions in a non-Hermitian field theory with local non-Abelian SU(2) gauge symmetry and a modified antilinear CPT symmetry. The solutions are obtained in a fourfold Bogomolny-Prasad-Sommerfield scaling limit giving rise to two different types of monopole masses that saturate the lower energy bound. These two masses only coincide in the Hermitian limit and in the limit in which the symmetry breaking vacuum tends to the trivial symmetry preserving vacuum. In the two theories corresponding to the two known Dyson maps these two masses are exchanged, unlike the Higgs and the gauge masses, which remain the same in both theories. We identify three separate regions in parameter space bounded by different types of exceptional points. In the first region the monopole masses are finite and tend both to zero at the boundary exceptional point, in the second the monopole masses become complex and in the third only one of the monopole masses becomes zero at the boundary exceptional point, whereas the other tends to infinity. We find a self-dual point in parameter space at which the gauge mass becomes exactly identical to the monopole mass.

中文翻译：

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非厄米量子场论中的 't Hooft-Polyakov 单极子

我们在具有局部非阿贝尔 SU(2) 规范对称性和修正的反线性 CPT 对称性的非厄米场论中构建了精确的 t Hooft-Polyakov 单极解。解决方案是在四倍 Bogomolny-Prasad-Sommerfield 标度极限中获得的，从而产生两种不同类型的单极子质量，它们使能量下限饱和。这两个质量仅在厄米极限和对称破缺真空趋向于平凡对称保持真空的极限重合。在对应于两个已知戴森图的两种理论中，这两个质量是交换的，不像希格斯和规范质量，它们在两种理论中都保持不变。我们在由不同类型的异常点界定的参数空间中识别三个独立的区域。在第一个区域中，单极子质量是有限的，并且在边界异常点处都趋于零，在第二个区域中，单极子质量变得复杂，在第三个区域中，只有一个单极子质量在边界异常点处变为零，而另一个则趋于到无穷远。我们在参数空间中找到一个自对偶点，在该点处规范质量与单极质量完全相同。