The non-abelian self-dual string

Christian Sämann*, Lennart Schmidt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
59 Downloads (Pure)


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
Publication statusE-pub ahead of print - 18 Dec 2019


  • 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


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