# The Non-Abelian Self-Dual String and the (2,0)-Theory

## TL;DR

This paper develops a non-abelian generalization of the self-dual string using the string 2-group, deriving equations of motion, explicit solutions, and connecting to six-dimensional superconformal field theory and 4D Yang-Mills.

## Contribution

It introduces the string 2-group as the gauge structure for non-abelian self-dual strings and provides explicit solutions and connections to higher-dimensional theories.

## Key findings

- Explicit solution analogous to 't Hooft-Polyakov monopole
- Solution is globally defined on r^4 and approaches abelian case
- Equations arise as BPS equations in 6D superconformal theory

## Abstract

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.