We argue that the relevant higher gauge group for the non-abelian generalization of the self-dual string equation is the string 2-group. We then derive the corresponding equations of motion and discuss their properties. The underlying geometric picture is a string structure, i.e., a categorified principal bundle with connection whose structure 2-group is the string 2-group. We readily write down the explicit elementary solution to our equations, which is the categorified analogue of the ’t Hooft–Polyakov monopole. Our solution passes all the relevant consistency checks; in particular, it is globally defined on $$\mathbb {R}^4$$ R 4 and approaches the abelian self-dual string of charge one at infinity. We note that our equations also arise as the BPS equations in a recently proposed six-dimensional superconformal field theory and we show that with our choice of higher gauge structure, the action of this theory can be reduced to four-dimensional supersymmetric Yang–Mills theory.

中文翻译：

---

非阿贝尔自对偶弦

我们认为，自对偶弦方程的非阿贝尔推广的相关更高规范群是弦 2-群。然后我们推导出相应的运动方程并讨论它们的性质。底层的几何图形是一个弦结构，即具有连接的分类主丛，其结构2-群是弦2-群。我们很容易写出方程的显式初等解，它是 't Hooft-Polyakov 单极子的分类模拟。我们的解决方案通过了所有相关的一致性检查；特别是，它在 $$\mathbb {R}^4$$ R 4 上全局定义并且在无穷远处接近阿贝尔自对偶电荷一串。