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The non-abelian self-dual string
Letters in Mathematical Physics ( IF 1.371 ) Pub Date : 2019-12-18 , DOI: 10.1007/s11005-019-01250-3
Christian Sämann, Lennart Schmidt

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 \(\mathbb {R}^4\) 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.
更新日期:2019-12-18

 

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