BREAKING OF TOPOLOGICAL SYMMETRY

The coupling of topological matter to topological Yang-Mills theory in four dimensions is considered and a model is presented. It is shown t hat, contrary to the two-dimensional case, this coupling may lead to a breaking of the topological symmetry. This means that the vacuum expe ctation 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 couplin g.