### 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 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.

Original language | English |
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Journal | Letters in Mathematical Physics |

Early online date | 18 Dec 2019 |

DOIs | |

Publication status | E-pub ahead of print - 18 Dec 2019 |

### Fingerprint

### Keywords

- Higher gauge theory
- Self-dual strings
- String group
- Strong homotopy lie algebras
- Superconformal field theories

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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**The non-abelian self-dual string.** / Sämann, Christian; Schmidt, Lennart.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The non-abelian self-dual string

AU - Sämann, Christian

AU - Schmidt, Lennart

PY - 2019/12/18

Y1 - 2019/12/18

N2 - 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 R4 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.

AB - 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 R4 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.

KW - Higher gauge theory

KW - Self-dual strings

KW - String group

KW - Strong homotopy lie algebras

KW - Superconformal field theories

UR - http://www.scopus.com/inward/record.url?scp=85077046487&partnerID=8YFLogxK

U2 - 10.1007/s11005-019-01250-3

DO - 10.1007/s11005-019-01250-3

M3 - Article

AN - SCOPUS:85077046487

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

ER -