Higher Poincare Lemma and Integrability

Getachew Alemu Demessie, Christian Saemann

Research output: Contribution to journalArticle

7 Citations (Scopus)
37 Downloads (Pure)

Abstract

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a proof by Voronov and yields the explicit gauge parameters connecting a flat local connective structure to the trivial one. Finally, we show how higher flatness appears as a necessary integrability condition of a linear system which featured in recently developed twistor descriptions of higher gauge theories.
Original languageEnglish
Article number082902
JournalJournal of Mathematical Physics
Volume56
Issue number8
DOIs
Publication statusPublished - 28 Aug 2015

Keywords

  • hep-th
  • math-ph
  • math.DG
  • math.MP

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