Duality in the Context of Topological Quantum Field Theory

Abstract

We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and their relation to the Donaldson invariants. In addition, we analyze the fruitful framework that this connection has originated. This analysis involves the study of topological quantum field theories which contain twisted N=2 supersymmetric matter fields as well as theories obtained after twisting N=4 supersymmetry. In the latter case, we present some recent results including the generalization of the partition function of the Vafa-Witten theory for gauge group SU(N) with prime N.