The non-abelian self-dual string

Christian Sämann, Lennart Schmidt

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
JournalLetters in Mathematical Physics
Early online date18 Dec 2019
DOIs
Publication statusE-pub ahead of print - 18 Dec 2019

Fingerprint

strings
Strings
Principal Bundle
Gauge Group
Monopole
Yang-Mills Theory
monopoles
infinity
Field Theory
bundles
Equations of Motion
Gauge
equations of motion
Charge
Infinity
analogs
Analogue

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

In: Letters in Mathematical Physics, 18.12.2019.

Research output: Contribution to journalArticle

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