Higher Poincare Lemma and Integrability
High Energy Physics - Theory
2015-08-31 v2 Mathematical Physics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.1406.5342,
title = {Higher Poincare Lemma and Integrability},
author = {Getachew Alemu Demessie and Christian Saemann},
journal= {arXiv preprint arXiv:1406.5342},
year = {2015}
}
Comments
1+21 pages, presentation streamlined, section on integrability for higher linear systems significantly improved, published version