4-DIMENSIONAL YANG-MILLS THEORY AS A DEFORMATION OF TOPOLOGICAL BF THEORY

The classical action for pure Yang-Mills gauge theory can be formulate d as a deformation of the topological BF theory where, beside the two- form field B, one has to add one extra-field eta given by a one-form w hich transforms as the difference of two connections. The ensuing acti on functional gives a theory that is both classically and quantistical ly equivalent to the original Yang-Mills theory. In order to prove suc h an equivalence, it is shown that the dependency on the field eta can be gauged away completely. This gives rise to a field theory that, fo r this reason, can be considered as semi-topological or topological in some but not all the fields of the theory. The symmetry group involve d in this theory is an affine extension of the tangent gauge group act ing on the tangent bundle of the space of connections. A mathematical analysis of this group action and of the relevant BRST complex is disc ussed in detail.