Gauge Group TQFT and Improved Perturbative Yang-Mills Theory

TL;DR

This paper reinterprets gauge fixing in Yang-Mills theories as a topological quantum field theory, linking gauge ambiguities to supersymmetry breaking and providing a gauge-invariant way to handle zero modes, with implications for Green functions.

Contribution

It introduces a novel topological gauge-fixing framework for Yang-Mills theories that addresses ambiguities and zero modes without breaking symmetries, improving perturbative analysis.

Findings

Gauge-fixing ambiguities relate to supersymmetry breaking.

Zero modes are handled via equivariant cohomology.

Power corrections to Green functions are gauge invariant.

Abstract

We reinterpret the Faddeev-Popov gauge-fixing procedure of Yang-Mills theories as the definition of a topological quantum field theory for gauge group elements depending on a background connection. This has the advantage of relating topological gauge-fixing ambiguities to the global breaking of a supersymmetry. The global zero modes of the Faddeev-Popov ghosts are handled in the context of an equivariant cohomology without breaking translational invariance. The gauge-fixing involves constant fields which play the role of moduli and modify the behavior of Green functions at subasymptotic scales. At the one loop level physical implications from these power corrections are gauge invariant.