On the renormalization of topological Yang-Mills field theory in N=1 superspace

We discuss the renormalization aspects of topological super-Yang-Mills field theory in N = 1 superspace. Our approach makes use of the regularization-independent BRS algebraic technique adapted to the case of an N = 1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be a BRS coboundary, implying that the cohomological properties of the supertopological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik beta-function of the model by employing a recently discovered supersymmetric antighost Ward identity.