Breaking of Topological Symmetry

TL;DR

This paper investigates how coupling topological matter to topological Yang-Mills theory in four dimensions causes a breaking of topological symmetry, affecting the invariance of observable vacuum expectation values under metric deformations.

Contribution

It introduces a four-dimensional model showing that coupling topological matter to Yang-Mills theory breaks topological symmetry, unlike in two dimensions.

Findings

Coupling leads to symmetry breaking in four dimensions.

Vacuum expectation values lose invariance under metric deformations.

The action retains all original symmetries despite symmetry breaking.

Abstract

The coupling of topological matter to topological Yang-Mills theory in four dimensions is considered and a model is presented. It is shown that, contrary to the two-dimensional case, this coupling leads to a breaking of the topological symmetry. This means that the vacuum expectation values of the observables of the theory loose their invariance under small deformations of the metric while the action of the model possesses all the symmetries corresponding to the case with no coupling.