Variational cohomology and topological solitons in Yang-Mills-Chern-Simons theories

TL;DR

This paper uncovers a non-trivial cohomological obstruction in Yang-Mills-Chern-Simons theories on certain manifolds, leading to strong non-existence results for topological solitons and instantons, with implications for holographic QCD.

Contribution

It demonstrates the existence of a non-trivial cohomological obstruction in Yang-Mills-Chern-Simons theories, challenging previous assumptions of vanishing obstructions in physics.

Findings

Identifies a non-trivial obstruction in odd-dimensional Yang-Mills-Chern-Simons theories

Proves a strong non-existence theorem for topological solitons/instantons

Discusses implications for holographic QCD models

Abstract

In cohomological formulations of the calculus of variations obstructions to the existence of (global) solutions of the Euler-Lagrange equations can arise in principle. It seems, however, quite common to assume that such obstructions always vanish, at least in the cases of interest in theoretical physics. This is not so: for Yang-Mills-Chern-Simons theories on compact manifolds in odd dimensions $\geq 5$ we find a non trivial obstruction which leads to a quite strong non existence theorem for topological solitons/instantons. The consequences of this result for the Yang-Mills-Chern-Simons theories of holographic QCD (on $I\!\!R^{5}$) are discussed.