A cohomological obstruction in higher dimensional Chern--Simons gauge theories

TL;DR

This paper investigates cohomological obstructions that prevent the existence of global solutions to Euler-Lagrange equations in higher-dimensional Chern--Simons gauge theories, revealing new topological insights.

Contribution

It introduces a set of cohomology classes that act as obstructions in the variational calculus of higher-dimensional Chern--Simons theories.

Findings

Identification of specific cohomology classes as obstructions

Implications for the existence of global solutions

Enhanced understanding of topological structures in gauge theories

Abstract

We study a set of cohomology classes which emerge in the cohomological formulations of the calculus of variations as obstructions to the existence of (global) solutions of the Euler--Lagrange equations of Chern--Simons gauge theories in higher dimensions $2p+1 > 3$.