Topological Yang-Mills cohomology in pure Yang-Mills Theory

TL;DR

This paper reveals an embedded topological sector within pure Yang-Mills theory using the BFYM formalism, linking non-perturbative aspects to topological Yang-Mills theory and exploring topological observables.

Contribution

It demonstrates how to identify and analyze a topological sector in Yang-Mills theory through a field redefinition in the BFYM formalism, providing new insights into non-perturbative phenomena.

Findings

Embedded topological sector in Yang-Mills theory identified

Calculation of YM observables related to topological Yang-Mills observables

Discussion on describing topological observables within YM theory

Abstract

Using the first order formalism (BFYM) of the Yang-Mills theory we show that it displays an embedded topological sector corresponding to the field content of the Topological Yang-Mills theory (TYM). This picture arises after a proper redefinition of the fields of BFYM and gives a clear representation of the non perturbative part of the theory in terms of the topological sector. In this setting the calculation of the $vev$ of a YM observable is translated into the calculation of a corresponding (non topological) quantity in TYM. We then compare the topological observables of TYM with a similar set of observables for BFYM and discuss the possibility of describing topological observables in YM theory.