We show that a suitable background field can bring a non-BPS topological soliton into its BPS, self-dual, counterpart. As an example we consider Skyrmions in the minimal Skyrme model. We prove the triviality of the corresponding moduli space. This means that the resulting self-dual Skyrmion does statically interact with the background field. We also show that the originally self-dual Skyrmions (e.g. solutions of the BPS Skyrme model) can preserve the self-duality after a coupling with a background field. In this case, BPS Skyrmions can be effortless moved with respect to the background.

中文翻译：

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背景场和自双 Skyrmions

我们表明，合适的背景场可以将非 BPS 拓扑孤子带入其 BPS、自对偶、对应物。作为一个例子，我们在最小 Skyrme 模型中考虑 Skyrmions。我们证明了相应模空间的平凡性。这意味着由此产生的自双 Skyrmion 确实与背景场静态交互。我们还表明，最初的自对偶 Skyrmions（例如 BPS Skyrme 模型的解决方案）在与背景场耦合后可以保持自对偶。在这种情况下，BPS Skyrmions 可以毫不费力地相对于背景移动。