Work

Higher Poincaré lemma and integrability

Year: 2015

Type: article

Abstract: We prove the non-abelian Poincaré lemma in higher gauge theory in two different ways. That is, we show that every flat local connective structure is gauge trivial. The first method uses a result by Jacobowitz [J. Differ. Geom. 13, 361 (1978)] which states solvability conditions for differential equations of a certain type. The second method extends a proof by Voronov [Proc. Am. Math. Soc. 140, 2855 (2012)] 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.

Source: Journal of Mathematical Physics

DOI: 10.1063/1.4929537

Authors: G. A. Demessie, C. Sämann

Institutions: Heriot-Watt University, Maxwell Institute for Mathematical Sciences

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Engineering and Physical Sciences Research Council, Science and Technology Facilities Council